Profile creation method, profile creation program, and printing apparatus

ABSTRACT

A second chromaticity value feature is corrected and approximated to a first chromaticity value feature, a new limit value for an ink amount is determined based on the second chromaticity value feature after the approximation, optimization is performed by designating an ink amount which is equal to or less than the newly determined limit value when an ink amount reproducing a hue value represented by a lattice point is determined by the optimization of the ink amount with the use of an object function for evaluating image quality when the designated amount of ink is made to adhere to a first print medium, the ink amount determined by the optimization is converted with a conversion relationship based on the first chromaticity value feature and the second value chromaticity feature.

BACKGROUND

1. Technical Field

The present invention relates to a profile creation method, a profilecreation program, and a printing apparatus.

2. Related Art

A color conversion profile is information representing a correspondencerelationship between an input color system and an output color system,which is used in the form of a color conversion look-up table, a colorconversion function, or the like. A coordinate value of an input colorsystem in a color conversion look-up table indicates a position of apoint in a color space of the input color system, and a coordinate valueof an output color system indicates a position of a point in a colorspace of the output color system. In this specification, a point in anarbitrary color space will also be referred to as a “color point” or a“lattice point”. In addition, color point represented by an input valueand a color point represented by an output value registered in the colorconversion look-up table will also be referred to as an “input latticepoint” and an “output lattice point”, respectively.

As a technique for smoothing an arrangement of input lattice points andoutput lattice points in the color conversion look-up table, a techniquedescribed in JP-A-2006-197080 which has been disclosed by the presentapplicant can be exemplified. According to such smoothing, an optimalink amount for reproducing L*a*b* lattice points after movement isdetermined by optimization processing with the use of an object functionafter the movement of the lattice point in a Lab color system. Theoptimal ink amount is determined as an ink amount for minimizing theobject function.

However, since a color forming feature (hue value feature) with respectto the same ink amount is different for each kind of printing medium,and an ink amount (duty limit value) which can adhere to a unit area isalso different, there is a problem in that it is necessary to prepare anobject function for each kind of printing medium in order to create acolor conversion look-up table for a plurality of printing media.

Moreover, since an object function includes a term for evaluating animage quality based on a hue value of a color reproduced when eachamount of ink adheres to a printing medium, there is a problem in thatit is necessary to prepare a color prediction model, which is forpredicting a hue value based on an ink amount, for each kind of printingmedium. Preparation of a color prediction model and the like for everykind of printing media requires great effort and resources. Therefore,it can be considered that color prediction models for some kinds ofprinting media (basic media) are prepared in advance and hue valueprediction based on an ink amount is performed with the use of the colorprediction models prepared for the basic media when a color conversionlook-up table is created for every kind of printing media (divertingmedia) for which color prediction models have not been prepared. Thatis, prediction of a hue value based on an ink amount is executed withthe use of the color prediction models prepared for the basic media, anink amount is optimized by an object function based on the predicted huevalue, and a color conversion look-up table for diverting media iscreated based on the ink amount determined through the optimization.

However, a color forming feature with respect to an ink amount isdifferent for each printing medium as described above. Therefore, thereis a concern in that in a color conversion look-up table for divertingmedia, which is finally obtained by executing hue value prediction withthe use of the color prediction models prepared for the basic media andoptimization of the ink amount by the object function, a defined inkamount (output lattice points) is eccentrically located in a certaincolor region (for example, an ink amount which realizes a relativelydark color formation is prescribed as many output lattice points on thediverting media), for example. Such eccentric location of the latticepoints in the color conversion look-up table adversely affects latercolor management or further profile creation with the use of the colorconversion look-up table.

SUMMARY

An advantage of some aspects of the invention is to provide a techniquefor creating an optimal profile for various printing media withoutpreparing an object function and a color prediction model for eachprinting medium.

According to an aspect of the invention, there is provided a profilecreation method according to which a profile of defining an ink amountis created by determining an ink amount for reproducing a hue valueindicated by a lattice point in a device-independent color system, themethod including: firstly obtaining a first hue value featurerepresenting a variation in a hue value on a first print mediumcorresponding to a variation in an ink amount up to a limit value of anink amount which can adhere to the first print medium; secondlyobtaining a second hue value feature representing a variation in a huevalue in a second print medium, which is different from the first printmedium, corresponding to a variation in an ink amount up to a limitvalue of an ink amount which can adhere to the second print medium;determining a new limit value of the ink amount based on the second huevalue feature after approximation by correcting and approximating thesecond hue value feature to the first hue value feature; determining anink amount which is equal to or less than the newly determined limitvalue to execute the optimization when the ink amount for reproducingthe hue value indicated by the lattice point is determined by the inkamount optimization with the use of an object function for evaluatingimage quality when a designated amount of ink is made to adhere to thefirst print medium; and creating a profile for the second print medium,for which the converted ink amount has been defined, by converting theink amount determined by the optimization with a conversion relationshipbased on the first hue value feature and the second hue value feature.

With such a configuration, a new limit value for the ink amount isdetermined based on the hue value feature of the second print medium(second hue value feature) after approximation to the hue value featureof the first print medium (first hue value feature), and an ink amountis determined among the ink amounts which is equal to or less than thenew limit value when the ink amount is determined by the ink amountoptimization with the use of the object function for evaluating imagequality when the ink is made to adhere to the first print medium.Therefore, each ink amount after converting the thus determined inkamount based on the conversion relationship of the first hue valuefeature and the second hue value feature (each ink amount defined by theprofile for the second print medium) is an optimal ink amount forreproducing each hue value on the second print medium, and each huevalue (the lattice point in the device-independent color system)reproduced by each ink amount is less one-sided in the color space. Thatis, it is possible to create an optimal profile for the second printmedium. In addition, the first print medium corresponds to a basicmedium while the second print medium corresponds to a diverting medium.

It is preferable that in determining the limit value, the new limitvalue be determined based on a maximum value of the ink amount in thesecond hue value feature after the approximation.

With such a configuration, it is possible to determine an optimal limitvalue in consideration of creating a profile for the second print mediumwith the use of the optimization result as a limit value of the inkamount for optimizing the ink amount on the assumption of the firstprint medium.

It is preferable that in determining the restriction value, curves begenerated based on each reference point after displacement, bydisplacing a plurality of reference points in the second hue valuefeature in an ink amount direction, degrees of approximation between thegenerated curves and the first color hue value feature be evaluated, anda curve with the highest degree of approximation be regarded as thesecond hue value feature after the approximation.

With such a configuration, it is possible to easily obtain the secondhue value feature after the correction which approximates to the firsthue value feature.

It is preferable that in determining the restriction value, more weightat the time of evaluation be given to the reference points belonging toa specific hue value range than to the other reference points from amonga plurality of reference points on the curve and a degree ofapproximation between the curve and the first hue value feature beevaluated. More specifically, when the first hue value feature and thesecond hue value feature represent luminosity variations correspondingto variations in ink amounts, the weight may be given at least toreference points belonging to an intermediate luminosity region fromamong a plurality of reference points on the curve in determining thelimit value.

With such a configuration, it is possible to obtain the second hue valuefeature with a high degree of approximation with respect to the firsthue value feature within a specific hue value range for which gradationfeature is particularly valued. Therefore, it is possible to determinean optimal limit value in consideration of creating a profile for thesecond print medium with the use of the optimization result as the limitvalue of the ink amount when the ink amount optimization on theassumption of the first print medium is performed, by determining thenew limit value based on such a second hue value feature after theapproximation.

It is preferable that in determining the ink amount, a lattice point tobe restricted to an achromatic color be restricted to a hue valuedeviated from the achromatic color in a color phase direction based on atone difference between the first print medium and the second printmedium.

With such a configuration, it is possible to restrict an actual huevalue of a lattice point to an achromatic color in consideration of atone difference between the first print medium and the second printmedium.

The technical spirit of the invention can be realized as modes otherthan the profile creating method. For example, it is possible to coverthe invention of a profile creation apparatus provided with a unit ofrealizing the steps included in the profile creation method and theinvention of a profile creation program which causes a computer torealize the steps included in the profile creation method. In addition,the technical spirit of the invention includes a configurationcorresponding to the aforementioned profile creation apparatus and cancover the invention of a print control apparatus which controls aprinter as a printing apparatus by using the profile for colorconversion processing of image data and the inventions of the method andprogram corresponding to the print control apparatus. Furthermore, it isalso possible to cover a printing apparatus in which the profile createdas described above is embedded to be used for color conversionprocessing of image data (a printing apparatus causes an amount, whichis obtained by performing color conversion with reference to theprofile, of ink to adhere to a printing medium), a method and a programcorresponding to such a printing apparatus, and the invention of amanufacturing method for such a printing apparatus.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanyingdrawings, wherein like numbers reference like elements.

FIG. 1 is a block diagram showing a configuration of a profile creationapparatus according to an embodiment.

FIG. 2 is a flowchart showing an overall processing procedure accordingto an embodiment.

FIG. 3 is a diagram showing a weight designation UI image.

FIG. 4 is a diagram showing an example of a medium table MTB.

FIG. 5 is a diagram showing an example of a setting table STB.

FIG. 6 is a flowchart showing a base LUT creation processing procedureaccording to an embodiment.

FIGS. 7A to 7C are explanatory diagrams showing processing contents whena base 3D-LUT is created by Steps S100 to S300 in FIG. 6.

FIGS. 8A to 8C are explanatory diagrams showing correspondencerelationships between hue values in an RGB color system as an inputcolor system and hue values in a Lab color system.

FIGS. 9A to 9C are explanatory diagrams showing processing contents whena base 4D-LUT is created by Steps S100 to S300 in FIG. 6.

FIGS. 10A and 10B are explanatory diagram showing a creation method of acolor correction LUT with the use of a base LUT.

FIG. 11 is an explanatory diagram showing a dynamic model used insmoothing processing according to an embodiment.

FIG. 12 is a diagram showing a state in which lattice pointscorresponding to gray axis lattice points are restricted by a graytarget.

FIG. 13 is a flowchart showing typical processing procedure forsmoothing processing.

FIG. 14 is a flowchart showing a detailed procedure of Step T100 in FIG.13.

FIGS. 15A to 15D are explanatory diagram showing processing contents ofSteps T120 to T150 in FIG. 13.

FIG. 16 is a flowchart showing a detailed procedure of optimizationprocessing (Step T130 in FIG. 13).

FIG. 17 is a block diagram showing a configuration of a printeraccording to an embodiment of the invention.

FIG. 18 is a block diagram showing a software configuration of aprinter.

FIG. 19 is a diagram showing a medium feature designation UI image.

FIGS. 20A to 20C are diagrams showing an example of a state in which afirst hue value feature and a second hue value feature are normalizedand approximated.

FIGS. 21A to 21C are diagrams showing another example of a state inwhich a first hue value feature and a second hue value feature arenormalized and approximated.

FIG. 22 is a graph obtained by plotting diverting medium tones anddiverted medium tones in an a*b* plane.

FIG. 23 is a diagram showing a gray target when a diverting medium LUTis created.

FIG. 24 is a diagram showing an example of a state in which ink amountsare reduced.

FIG. 25 is a diagram showing an example of a state in which a first huevalue feature and a second hue value feature are approximated.

FIG. 26 is a diagram showing a medium feature designation UI imageaccording to a modified example.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Next, description will be given of an embodiment of the invention in thefollowing order.

A. Apparatus configuration and overall processing procedureB. Basic medium LUT processing procedure

B-1. Overall procedure

B-2. Dynamic model

B-3. Processing procedure for smoothing processing (smoothing andoptimization processing)

B-4. Content of optimization processing

C. Configuration of printing apparatusD. Diverting media LUT creation procedure

E. Modified Example A. APPARATUS CONFIGURATION AND OVERALL PROCESSINGPROCEDURE

FIG. 1 is a block diagram showing a configuration of a profile creationapparatus according to an embodiment of the invention. The profilecreation apparatus is a subject which executes a profile creationmethod. Main parts of the apparatus are substantially realized by acomputer 10. Specifically, a CPU 12 provided in the computer 10 realizeseach of the functions such as a base LUT creation module 100, a colorcorrection LUT creation module 200, an LUT creation condition settingmodule 700, and the like by a reading a program (a profile creationprogram or the like) stored on a hard disk drive (HDD) 400 and executingcomputation based on the program while developing the program on a RAM13. A display apparatus (a liquid crystal display, for example) which isnot shown in the drawing is connected to the computer 10 and performs UI(user interface) display necessary for each processing. Moreover, aninput apparatus (a keyboard and a mouse, for example) which is not shownin the drawing is connected to the computer 10, and informationnecessary for each processing is input via the input apparatus. Inaddition, a printer 20 (FIG. 17) and a colorimeter which is not shown inthe drawing are connected to the computer 10. Moreover, the computer 10is provided with a forward model converter 300. The forward modelconverter 300 is further provided with a spectral printing modelconverter 310 and a color calculation unit 320. The forward modelconverter 300 corresponds to a color prediction model. Functions of eachpart will be described later. The term “LUT” is an abbreviation oflook-up table as a kind of profile.

The base LUT creation module 100 includes an initial value settingmodule 120, a smoothing processing module 130, and a table creationmodule 140. The smoothing processing module 130 includes a color pointdisplacement module 132, an ink amount optimization module 134, and animage quality evaluation index converter 136. The LUT creation conditionsetting module 700 is provided with an ink amount converter 710, a UImodule 720, and a setting information storage module 730. The settinginformation storage module 730 manages a medium table MTB and a settingtable STB stored on the HDD 400. The functions of each part will bedescribed later.

The HDD 400 is a storage apparatus for storing an inverse model initialLUT 410, a base 3D-LUT 510, a base 4D-LUT 520, a color correction 3D-LUT610, a color correction 4D-LUT 620, and the like. However, LUTs otherthan the inverse model initial LUT 410 are created by the base LUTcreation module 100 or the color correction LUT creation module 200. Thebase 3D-LUT 510 is a color conversion look-up table in which an RGBcolor system is an input and an ink amount is an output. The base 4D-LUT520 is a color conversion look-up table in which a CMYK color system isan input and an ink amount is an output. In addition, “3D” and “4D”represent the number of input values. The RGB color system and the CMYKcolor system as input color systems of the base LUTs 510 and 520 are notso-called device-dependent color systems but virtual color systems (orabstract color systems) not set in relation to a specific device. Thebase LUTs 510 and 520 are used for creating color correction LUTs 610and 620, for example. The “base LUT” is named because the look-up tableis used as a base for creating a color correction LUT. In addition, the“base LUT” corresponds to a “profile” created by the profile creationmethod according to an embodiment of the invention. The color correctionLUTs 610 and 620 are look-up tables for converting standarddevice-dependent color systems (an sRGB color system, a JAPAN COLOR 2001color system, for example) into an ink amount of a specific printer.Description will be given later of the inverse model initial LUT 410. Inthis embodiment, an LUT for a printer capable of using four kinds of inkincluding cyan (C), magenta (M), yellow (Y), and black (K). Although thefour kinds of ink are assumed in this embodiment for simplicity ofexplanation, it is also possible to apply an embodiment of the inventionto a case in which an LUT for other kinds of ink is created.

FIG. 2 is a flowchart showing an overall processing procedure accordingto this embodiment, which is executed by the computer 10. In Step S01,UI module 720 of the LUT creation condition setting module 700 receivesdesignation of a medium, for which it is desired to create an LUT, viathe display apparatus and the input apparatus. The UI module 720displays a list of each medium and causes the display apparatus todisplay a medium selection UI image from which a user is allowed toselect a desired medium. For example, the user can select a basic glosspaper, a basic matte paper, a basic normal paper, a basic proof paper,or the like as a basic medium. The term “basic medium” means a printingmedium provided by a printer manufacturer, for example, and particularlyprinting media for which the forward model converter 300 (spectralprinting model converter 310) and the image quality evaluation indexconverter 136 are prepared in advance in the embodiment of theinvention. Features of the basic medium are known, and data specifying acolor forming feature and a duty limit value when ink is made to adhereto each basic medium is stored in advance on the medium table MTB. Thebasic gloss paper, the basic matte paper, the basic normal paper, andthe basic proof paper respectively belongs to a gloss paper group, amatte paper group, a normal paper group, and a proof group.

On the other hand, in the medium selection UI image, it is possible toselect a gloss paper group sheet, a matte paper group sheet, a normalpaper group sheet, a proof group sheet, a non-classified sheet, or thelike as a diverting medium according to an embodiment of the inventionas well as a basic medium. The “diverting media” means printing mediawhich is not the same as any of the basic media and particularlyprinting media for which the forward model converter 300 (spectralprinting model converter 310) and the image quality evaluation indexconverter 136 are not prepared in advance in the embodiment of theinvention. When the user recognizes a group of a medium for which an LUTis created, it is possible to select a medium of the group. When theuser does not recognizes the group of the medium, or it is difficult toclassify the medium, it is possible to select a non-classified sheet. Inaddition, another configuration is also applicable in which the userdoes not designate a medium and a group of a medium is automaticallydetermined based on a color phase obtained by performing colormeasurement on the medium. If the medium as a target of LUT creation isdesignated, information specifying the medium is registered in thesetting table STB (Step S02).

In Step S03, the LUT creation condition setting module 700 obtains adefault weight w_(L*), w_(a*) . . . corresponding to the designatedmedium with reference to the medium table MTB stored on the HDD 400. Themedium groups include a gloss paper group, a matte paper group, a normalpaper group, a proof group, and a non-classified group, and the defaultweight w_(L*), w_(a*) . . . for each group is stored on the medium tableMTB. In Step S04, the UI module 720 causes the display apparatus todisplay a weight designation UI image and causes the input apparatus toreceive designation of weight w_(L*), w_(a*) . . . .

FIG. 3 shows the weight designation UI image, and

FIG. 4 shows an example of the medium table MTB. In the weightdesignation UI image, designation of weight w_(L*), w_(a*) . . . (0 to100%) for each term constituting an object function E which will bedescribed later is received. As shown in the drawing, a slider bar isprovided for each of the setting items including a feature ofgranularity, color constancy, running cost, gamut, and a gradationfeature, and increased weight is set for individual items if individualpointers are made to slide to the right side. In addition, a centerposition of the slider bar corresponds to a center value (50%) of theweight w_(L*), w_(a*) . . . . If a pointer for the feature ofgranularity in the weight designation UI image is made to slide to thefurther right side, an increased value of weight w_(GI) is set. If apointer for the color constancy is made to slide to the further rightside, an increased value of weight w_(CII(A)) . . . w_(CII(F12)) is set.In this embodiment, the value of weight w_(CII(A)) . . . w_(CII(F12)) isequally set. It is a matter of course that the value of weightw_(CII(A)) . . . w_(CII(F12)) may be differentiated depending on theimportance of the light source. If a pointer for the running cost ismade to slide to the further right side, an increased value of weightw_(TI) is set. If a pointer for the gamut is made to slide to thefurther right side, an increased value of weight w_(GMI) is set. If apointer for the gradation feature is made to slide to the further rightside, an increased value of w_(L*), w_(a*), w_(b*) is set. In thisembodiment, the value of weight w_(L*), w_(a*), w_(b*) is equally set.In addition, another configuration is also applicable in which it ispossible to set a different weight w_(L*), w_(a*), w_(b*) for each ofluminosity L* and chromaticities a*, b*. A position of a pointer and avalue of weight w_(L*), w_(a*) . . . may be in a relationship ofmonotonic increase and can be defined as various functions such as alinear function, quadratic function, and the like.

In Step S04, an initial position of each pointer when the slider barsare firstly displayed is a position corresponding to the default weightw_(L*), w_(a*) . . . obtained from the medium table MTB in Step S03. Asthe default weight w_(L*), w_(a*) a preferable value is set in advancefor each group of the media in the medium table MTB. As shown in FIG. 4,for the normal paper group, the default weight w_(TI) for the runningcost is set to be greater than the center value, the default weightw_(GMI) for the gamut is set to be smaller than the center value, andthe others are set to the center values. For the matte paper group andthe non-classified group, the default weight w_(L*), w_(a*) . . . forall items are set to the center values. For the gloss paper group, theweight w_(GI) the weight w_(L*), w_(a*), w_(b*), and the weight w_(GMI)for the feature of granularity, the gradation feature, and the gamut areset to be greater than the center values, and the others are set to thecenter values. For the proof paper group, only the weight w_(an) forgamut is set to be greater than the center value, and the others are setto the center values. If an enter button in the weight designation UIimage is clicked without changing the initial positions of the pointersby the user, the default weight obtained w_(L*), w_(a*) . . . in StepS03 is set as it is.

Since the default weight w_(L*)*, w_(a*) . . . is set to a preferablevalue in consideration of a use purpose of the medium of each group, itis not basically necessary to change. When the user particularly intendsto change the weight, it is possible to set desired weight w_(L*),w_(a*) . . . by sliding the pointers from initial positions to desiredpositions. In addition, as for each weight w_(L*), w_(a*) . . . , arelative size difference has meaning, and uniform increase or decreaseas a whole does not have much meaning. Accordingly, a configuration isalso applicable in which when a pointer for a certain item is displaced,pointers for the other items are uniformly displaced in the oppositedirection. In Step S05, the setting information storage module 730registers in the setting table STB the weight w_(L*), w_(a*) . . .corresponding to the position of each pointer when the enter button inthe weight designation UI image is clicked.

In Step S06, it is determined whether or not the medium designated inStep S01 is a basic medium, and a duty limit value for the basic mediumis obtained with reference to the medium table MTB in the case of thebasic medium (Step S07). In this embodiment, the four kinds of CMYK inkare discriminated by subscript j (j=1 to 4) of a natural number, andindividual ink amounts I₁ to I₄ to adhere to the medium are representedby vectors I=(I₁, I₂, I₃, I₄). The ink amount I_(j) (includingI_(j(R,G,B)), ΔI_(j), I_(jr), and h_(j) which will be described later)represented with no subscript j means a matrix (vector) including inkamount I_(j) of each ink as each. Moreover, the subscript j (j=5 to 7)represents an ink amount of a secondary color when two kinds among threekinds of CMY ink are mixed. That is, it is assumed that I₅=I₁+I₂,I₆=I₁+I₃, I₇=I₂+I₃. The ink amounts I₅ to I₇ respectively reproducescolors corresponding to color phases of blue (B), red (R), and green (G)on the medium. Furthermore, the subscript j (j=8) represents an inkamount when all the four kinds of CMYK ink are mixed. That is, it isassumed that I₈=I₁+I₂+I₃+I₄.

In this embodiment, the ink amount I₃ of each ink is expressed by 8bits. As shown in FIG. 4, the duty limit value D_(Ij) is stored for eachindividual ink (primary color), the total of the ink as a secondarycolor, and the total of all the ink. The duty limit value D_(Ij) means amaximum ink amount which can adhere to a unit area with respect to eachbasic medium, and a lower limitation value at which ink bleeding occurs,for example, is set. Physical properties of ink droplets on the mediumare different depending on the combinations of the ink and the media,and duty limit values D_(Ij) which are different depending on thecombinations are set. In addition, since a physical property which isdifferent from that in an individual ink is exhibited even in a case inwhich a plurality of kinds of ink are mixed, the duty limit valuesD_(Ij) (j=1 to 8) are set not only for the primary color but also forthe secondary color (mixed color of two kinds of ink) and the total ofall the ink. If the duty limit value D_(Ij) can be obtained for thebasic medium, the setting information storage module 730 causes thesetting table STB to store the obtained duty limit value D_(Ij) in StepS08. Moreover, in Step S08, the setting table STB is made to store aninvalid flag indicating that the ink amount converter 710 is invalid. Inthis specification, it is assumed that a range of the subscript j in thecase of a simple description of an ink amount I_(j) is from 1 to 4 and arange of the subscript j in the case of a description of the duty limitvalue D_(Ij) is from 1 to 8.

FIG. 5 shows an example of the setting table STB. When a basic medium isdesignated, a kind of aforementioned designated medium, weight w_(L*),w_(a*) . . . , a duty limit value D_(Ij), an invalid flag, and a tone ofa gray target (a_(gt)*, b_(gt)*) are stored in the setting table STB. Inthe case of a basic medium, the tone of the gray target (a_(gt)*,b_(gt)*) is set to (0, 0). On the other hand, when a diverting medium isdesignated, processing (from Step S09) which is different from thatdescribed above is executed. However, description will be firstlycompleted of the processing for creating an LUT when the basic medium isdesignated.

B. BASIC MEDIUM LUT PROCESSING PROCEDURE

B-1. Overall procedure

FIG. 6 is a flowchart showing a procedure for creating a basic mediumbase LUT by the computer 10 according to the embodiment. FIGS. 7 A to 7Care explanatory diagrams showing processing contents when a base 3D-LUTis created by Steps S100 to S300 in FIG. 6. In Step S100, the forwardmodel converter 300, the inverse model initial LUT 410, and the imagequality evaluation index converter 136 are prepared (activated) based oninformation stored on the setting table STB. As described above, sincethe spectral printing model converter 310 and the image qualityevaluation index converter 136 for the basic medium are prepared inadvance for the basic media, the spectral printing model converter 310and the image quality evaluation index converter 136 are activated andbrought into available states. In addition, since the invalid flag isadded to the setting table STB, the ink amount converter 710 is notactivated. Here, the “forward model” means a conversion model whichconverts the ink amount into a hue value of a device-independent colorsystem (predicts a color measurement value from an ink amount). On theother hand, the “inverse model” means a conversion model which convertsa hue value of a device-independent color system into an ink amount. Inthis embodiment, a CIE-Lab color system is used as a device-independentcolor system. Hereinafter, a hue value of the CIE-Lab color system willbe simply referred to as an “L*a*b* value” or an “Lab value”.

As shown in FIG. 7A, the spectral printing model converter 310constituting a former stage of the forward model converter 300 convertsink amounts I_(j) of a plurality of kinds of ink into spectralreflectivity R(λ) of color patches formed so as to adhere to acorresponding basic media. In addition, the term “color patch” in thisspecification is widely used to indicate not only a chromatic patch butalso an achromatic patch. In addition, “print” indicates that ink ismade to adhere to a medium in accordance with ink amounts. In thespectral printing model converter 310, the ink amounts I_(j) of theaforementioned four kinds of ink are inputs. The color calculation unit320 calculates the hue values of the Lab color system from the spectralreflectivity R(λ). In the calculation of the hue values, a light source(for example, a standard light D50) selected in advance is used as anobservation condition of the color patch. In addition, as a method ofcreating the spectral printing model converter 310, it is possible toemploy a method described in JP-T-2007-511175, for example.

The inverse model initial LUT 410 is a look-up table in which the L*a*b*value is an input and the ink amount I_(j) is output. In the initial LUT410, an L*a*b* space is divided into a plurality of small cells, and anoptimal ink amount I_(j) is selected and registered for each small cell.The selection is made in consideration of an image quality of the colorpatch printed on the basic medium with the ink amount I_(j), forexample. In general, there are multiple combinations of ink amountsI_(j) for reproducing a certain L*a*b* value. Therefore, selection of anoptimal ink amount from a desired viewpoint such as an image quality orthe like is registered in the initial LUT 410 from among the multiplecombinations of the ink amounts I_(j) for reproducing substantially thesame L*a*b* values. The L*a*b* value as an input value of the initialLUT 410 is a representative value of each small cell. On the other hand,an ink amount I_(j) as an output value reproduces one of the L*a*b*values in the cell. Accordingly, in the initial LUT 410, the L*a*b*value as an input value and the ink amount as an output value are notexactly in a correspondence relationship, and a value which is slightlydifferent from the input value of the initial LUT 410 is obtained whenthe ink amount as an output value is converted into an L*a*b* value withthe forward model converter 300. However, an initial LUT 410 in which aninput value and an output value are completely in a correspondencerelationship may be used. In addition, it is also possible to create abase LUT without using the initial LUT 410. In addition, as a method ofcreating the initial LUT 410 by selecting an optimal ink amount for eachsmall cell, it is possible to employ a method described in theJP-T-2007-511175, for example. According to the method described inJP-T-2007-511175, the spectral printing model converter 310 and theinverse model initial LUT 410 are created by forming a color patch onthe target printing medium. That is, in order to create a basic mediabase LUT, the spectral printing model converter 310 and the inversemodel initial LUT 410 created by forming a color patch on the basicmedium are prepared.

In Step S200 in FIG. 6, the initial input value for creating the baseLUT is set by the user. FIG. 7B shows an example of a configuration ofthe base 3D-LUT 510 and the initial input value setting thereof. Asinput values of the base 3D-LUT 510, values determined in advance asvalues of RGB at substantially equal intervals are set. Since it isconsidered that one group of RGB values represents a point in the RGBcolor space, one group of RGB values will also be referred to as an“input lattice point”. In Step S200, initial values of the ink amountsI_(j) for a few of input lattice points selected in advance from amongthe plurality of input lattice points are input by the user. In thisembodiment, all (17³) input lattice points which satisfy (R, G,B)=(16n₁-1, 16n₂-1, 16n₃-1) when each value of RGB is expressed by 8bits are selected. Here, it is assumed that n₁ to n₃ are integers from 0to 16, and R, G, B=0 when R, G, B=−1. The input lattice points for whichinitial input values are set include input lattice points correspondingto vertexes of a three-dimensional color solid in the RGB color space.At the vertexes of the three-dimensional color solid, each value of RGBbecomes a minimum value or a maximum value in the defined ranges.Specifically, for eight input lattice points including (R, G, B)=(0, 0,0), (0, 0, 255), (0, 255, 0), (255, 0, 0), (0, 255, 255), (255, 0, 255),(255, 255, 0), and (255, 255, 255), initial input values of the inkamounts I_(j) are set. In addition, seventeen input lattice pointssatisfying n₁=n₂=n₃ (hereinafter, described as gray lattice points) arepresent on a gray axis on the RGB color space. Moreover, all ink amountsI_(j) with respect to the input lattice points satisfying (R, G,B)=(255, 255, 255) are set to zero. The ink amounts I_(j) with respectto the other input lattice points are arbitrary and set to zero, forexample. In the example of FIG. 7B, an ink amount with respect to aninput lattice point (R, G, B)=(0, 0, 32) is a value other than zero,which is a value when this LUT 510 is completed.

In Step S300 in FIG. 6, the smoothing processing module 130 (FIG. 1)executes smoothing processing (smoothing and optimization processing)based on the initial input values set in Step S200. FIG. 7C shows aprocessing content in Step S300. On the left side in FIG. 7C, adistribution of a plurality of hue values in a state before thesmoothing processing is shown by double circles and white circles. Thehue values constitute a three-dimensional color solid CS in the L*a*b*space. The L*a*b* coordinate values of the hue values are'valuesobtained by converting ink amounts with respect to a plurality of inputlattice points in the base 3D-LUT 510 into the L*a*b* values with theuse of the forward model converter 300 (FIG. 7A). As described above,initial input values for the ink amounts are set only for a few ofpartial input lattice points in Step S200. Thus, initial values for theink amounts with respect to the other input lattice points are set basedon the initial input values by the initial value setting module 120(FIG. 1). The initial value setting method will be described later.

The color three-dimensional color solid CS of the Lab color system hasthe following eight vertexes (double circles in FIG. 7C):

a paper black point corresponding to a point P_(K): (R, G, B)=(0, 0, 0);

a paper white point corresponding to a point P_(W): (R, G, B)=(255, 255,255);

a cyan point corresponding to a point P_(C): (R, G, B)=(0, 255, 255);

a magenta point corresponding to a point P_(M): (R, G, B) (255, 0, 255);

a yellow point corresponding to a point P_(Y): (R, G, B)=(255, 255, 0);

a red point corresponding to a point P_(R): (R, G, B)=(255, 0, 0);

a green point corresponding to a point P_(G): (R, G, B)=(0, 255, 0); and

a blue point corresponding to a point P_(B): (R, G, B)=(0, 0, 255).

The right side in FIG. 7C shows a distribution of lattice points (huevalues) after the smoothing processing. The smoothing processing isprocessing in which the plurality of lattice points in the L*a*b* spaceis displaced to smooth the distribution of the lattice points to belocated at substantially equal intervals. In the smoothing processing,an optimal ink amount for reproducing an L*a*b* value of each latticepoint after the displacement is further determined. If the optimal inkamount is registered as an output value of the base LUT 510, the baseLUT 510 is completed.

FIG. 8A to 8C show correspondence relationships between lattice pointsin the input color system (namely, input lattice points) and the latticepoints in the Lab color system. The vertexes of the three-dimensionalcolor solid CS for the Lab color system have one-to-one correspondencerelationships with the vertex of the three-dimensional color solid forthe input color system in the base LUT 510. In addition, it is possibleto consider that sides (ridge lines) connecting each vertex alsomutually have correspondence relationships between both color solids.The hue value of each lattice point in the Lab color system before thesmoothing processing is respectively associated with the input latticepoint in the base LUT 510, and therefore, the hue value of each latticepoint in the Lab color system after the smoothing processing is alsorespectively associated with the input lattice point in the base LUT510. In addition the input lattice points in the base LUT 510 is notchanged through the smoothing processing. The three-dimensional colorsolid CS for the Lab color system after the smoothing processingcorresponds to an entirety of a color region which can be reproduced byan ink set constituting the output color system in the base LUT 510.Therefore, the input color system in the base LUT 510 has meaning as acolor system representing the entirety of the color region which can bereproduced with the ink set.

The smoothing processing is performed on the L*a*b* space when the baseLUT 510 is created for the following reason. As for the base LUT 510,there is a demand of setting the ink amount I_(j) of the output colorsystem so as to reproduce a color region which is as large as possible.On the other hand, a color region which can be reproduced on a mediumwith a specific ink set depends on a duty limit value or the like uniqueto the medium. Thus, it is possible to determine a color region whichcan be reproduced with a specific ink set if a range available for thehue values in the L*a*b* space is determined in consideration ofrestriction conditions such as the duty limit value D_(Ij) during thesmoothing processing. In addition, an algorithm for the displacement ofthe lattice points with the use of a dynamic model which will bedescribed later is used, for example.

In Step S400 in FIG. 6, the table creation module 140 creates the baseLUT 510 with the use of the result of the smoothing processing. That is,the table creation module 140 registers the optimal ink amount I_(j) forreproducing the hue values of the lattice points in the Lab color systemrespectively associated with the input lattice points, as an outputvalue of the base LUT 510. In addition, it is also possible to select asprocessing targets only hue values of the lattice points correspondingto a part of the input lattice points in the base LUT 510 in thesmoothing processing in order to reduce the calculation burden. Forexample, when an interval of the RGB values at the input lattice pointsin the base LUT 510 is 16, it is possible to reduce burden of thesmoothing processing to the half if the interval of the RGB values atthe input lattice points as the targets of the smoothing target is setto 32. In such a case, the table creation module 140 determines andregisters ink amounts I_(j) with respect to all input lattice points inthe base LUT 510 by interpolating the result of the smoothingprocessing.

FIG. 9A to 9C are explanatory diagrams showing processing contents whena base 4D-LUT 520 is created by Steps S100 to S300 in FIG. 6. FIG. 9A isthe same as FIG. 7A. The base 4D-LUT 520 shown in FIG. 9B is differentfrom the base 3D-LUT 510 shown in FIG. 7B in that an input is the MYKcolor system. As initial input values of the base 4D-LUT 520, ink amountinitial values are set for sixteen input lattice points including (C, M,Y, K)=(0, 0, 0, 0), (0, 0, 255, 0), (0, 255, 0, 0), (0, 255, 255, 0),(255, 0, 0, 0), (255, 0, 255, 0), (255, 255, 0, 0), (255, 255, 255, 0),(0, 0, 0, 255), (0, 0, 255, 255), (0, 255, 0, 255), (0, 255, 255, 255),(255, 0, 0, 255), (255, 0, 255, 255), (255, 255, 0, 255), and (255, 255,255, 255). The initial input values of the ink amounts with respect tothe other input lattice points are arbitrary and set to zero, forexample. In this embodiment, it is assumed that seventeen gray latticepoints on the gray axis where C=M=Y is satisfied are included as inputlattice points even in the case of creating the base 4D-LUT 520.

FIG. 9C shows a state of the smoothing processing. As a color solidcorresponding to the base 4D-LUT 520 in the L*a*b* space, onethree-dimensional color solid CS is present with respect to each of theK values among the input values as shown in the right end of FIG. 9C. Inthis example, a plurality of color solids CS including a color solid ofK=0 and a color solid of K=32 are shown. In this specification, suchindividual color solids CS will also be referred to as “K layers”. Thisis because it is possible to consider that each color solid correspondsto an input layer in which a K value is constant while C, M, and Yvalues are variable among the CMYK values. The plurality of color solidsXS expresses darker color regions as the K values become greater. Theplurality of color solids CS can be realized by determining the inkamounts of the black ink K such that the ink amounts I₄ become larger asthe K values in the input color systems are greater. As described above,the reproducible color region is restricted by the duty limit valueD_(Ij) and the like. The duty limit value D_(Ij) depends on a type of adesignated medium. On the other hand, as a method for reproducing darkcolors, a method with the use of an achromatic ink such as black ink Kor the like and a method with the use of composite black can beexemplified. However, in the case of the composite black, there is ahigher possibility of conflicting with the duty limit value as comparedwith the black ink K due to a larger total ink amount, which isdisadvantageous in reproducing dark colors. Accordingly, a color solidin which the K value in the input color system is larger and the inkamount I₄ of the black ink K is larger can reproduce further dark colorsthan a color solid in which the K value in the input color system issmaller and the ink amount I₄ of the dark black ink K is smaller.

FIGS. 10A and 10B are explanatory diagrams showing a creation method ofa color correction LUT which is executed by the color correction LUTcreation module 200 with the use of the base LUT. As shown in FIG. 10A,the base 3D-LUT 510 converts the RGB values into the ink amounts I_(j).The ink amounts I_(j) after the conversion is converted by the forwardmodel converter 300 into L*a*b* values. On the other hand sRGB valuesare converted into L*a*b* values based on a known conversion equation.The L*a*b* values after the conversion are subjected to gamut mappingsuch that the color region thereof coincides with the color region ofthe L*a*b* values converted by the forward model converter 300. On theother hand, an inverse conversion LUT 511 is created while the L*a*b*values converted from the RGB values via the base 3D-LUT 510 and theforward model converter 300 are regarded as an opposite directionlook-up table. The L*a*b* values which have been subjected to the gamutmapping are converted into RGB values by the inverse conversion LUT 511.The RGB values are further converted again into ink amounts I_(j) by thebase 3D-LUT 510. It is possible to create the color correction 3D-LUT610 by registering the correspondence relationships between the inkamounts converted again and the initial sRGB values. The colorcorrection 3D-LUT 610 is a color conversion table which converts an sRGBcolor system into an ink color system.

FIG. 10B shows a creation method of the color correction 4D-LUT 620,which is executed by the color correction LUT creation module 200. FIG.10B is different from FIG. 10A in that a 4D-LUT 520 and an inverseconversion LUT 521 thereof are used instead of the 3D-LUT 510 and theinverse conversion LUT 511 and in that a known conversion equation forconverting a JAPAN COLOR system (described as “jCMYK” in the drawing)into L*a*b* value is used instead of the known conversion equation forconverting the sRGB color system into L*a*b* values. As is well known,JAPAN COLOR is a color system configured by the four colors CMYK.According to the method shown in FIG. 10B, when the L*a*b* values areconverted into CMYK values in the inverse conversion LUT 521, a K layer(a part in which the K value becomes constant) of the inverse conversionLUT 521 is selected from the K value of the initial jCMYK values beforethe known conversion. Accordingly, it is possible to create the colorcorrection 4D-LUT 620 which reflects a feature in the K layer in thebase 4D-LUT 520. In addition, the setting information storage module 730adds the setting table STB to the created base LUTs 510 and 520 and thecolor correction LUTs 610 and 620. In so doing, it is possible toidentify for what kind of medium the base LUTs 510 and 520 and the colorcorrection LUTs 610 and 620 have been created and with what weightw_(L*), w_(a*) . . . the base LUTs 510 and 520 and the color correctionLUTs 610 and 620 have been created.

Generally, the base LUTs 510 and 520 are mounted on a printer driver andused for processing other than the color correction LUT creationprocessing, and other application example will be omitted here.Hereinafter, a dynamic model used in the smoothing processing (smoothingand optimization processing) in the embodiment will briefly bedescribed, and smoothing processing procedure and a content of theoptimization processing will then be described in this order.

B-2. Dynamic Model

FIG. 11 is an explanatory diagram showing a dynamic model used in thesmoothing processing (smoothing and optimization processing) accordingto the embodiment. Here, a state in which lattice points (white circlesand double circles) corresponding to the aforementioned input latticepoints are arranged in the L*a*b* color space is shown. However, thearrangement of the lattice points is depicted in a two-dimensionalmanner for convenience of explanation. In this dynamic model, it isassumed that virtual force F_(pg) of the following equation is appliedto a focused lattice point g.

$\begin{matrix}{\overset{\rightarrow}{{Fp}_{g}} = {{\overset{\rightarrow}{F_{g}} - {k_{v}\overset{\rightarrow}{V_{g}}}} = {{k_{p}{\sum\limits_{n = 1}^{N}\left( {\overset{\rightarrow}{X_{gn}} - \overset{\rightarrow}{X_{g}}} \right)}} - {k_{v}\overset{\rightarrow}{V_{g}}}}}} & (1)\end{matrix}$

Here, F_(g) represents a sum of attraction force, V_(g) represents aspeed vector of the focused lattice point g, −k_(v)V_(g) representsresistance force in accordance with a speed, X_(g) is a position vectorof the focused lattice point g, X_(gn) represents a position vector ofan adjacent lattice point gn, and k_(p), k_(v) represent coefficients.The coefficient sk_(p) and k_(v) are set in advance to predeterminedvalues. In the description, arrows representing vectors will be omitted.

This model is a damped oscillation model of mass points connected witheach other by a spring. That is, the virtual total force F_(pg) appliedto the focused lattice point g is a sum of spring force F_(g) whichbecomes greater when a distance between the focused lattice point g andthe adjacent lattice point gn is longer and resistance force −k_(v)V_(g)which becomes greater when a speed of the focused lattice point g ishigher. According to the dynamic mode, a speed vector V_(g) and aposition vector X_(g) after the elapse of a short time dt aresequentially calculated after setting initial values of the positionvector X_(g) and the speed vector V_(g) for each color point. Inaddition, the initial values of speed vectors for a plurality of colorpoint are set to zero, for example. If calculation (simulation) usingsuch a dynamic model is used, it is possible to obtain a smooth colorpoint distribution by gradually displacing each color point in theL*a*b* color space.

As force applied to each hue value, it is also possible to use forceother than the spring force F_(g) and the resistance force −k_(v)V_(g).For example, various kinds of force described in JP-A-2006-197080disclosed by the present applicant can be used in this dynamic model. Inaddition, it is also possible to handle specific hue values asrestricted points which are not displaced by a dynamic model when eachhue value is displaced by applying the dynamic model. In thisembodiment, hue values of the lattice points corresponding to theaforementioned seventeen gray axis lattice points are restricted so asto be deviated in a color phase direction represented by gray targettone (a_(gt)*, b_(gt)*). Since the gray target tone (a_(gt)*,b_(gt)*)=(0, 0) is designated in the case of a basic medium, the valuesof the lattice points corresponding to the gray axis lattice points arerestricted so as to show the positions on the L* axis in the L*a*b*color space.

FIG. 12 shows a state in which the positions (hue values) of the latticepoints corresponding to the gray axis lattice points are restricted by agray target. As shown in the drawing, the lattice points (white circles)corresponding to the gray axis lattice points are restricted so as toshow the positions at which a line segment (gray target) connecting thepaper black point and the paper white point on the L* axis in the L*a*b*color space is equally divided into sixteen parts. In addition, it ispossible to restrict specific lattice points to specific positions inthe L*a*b* color space by a method disclosed in JPA-2006-217150. Byuniformly restricting the lattice points on the L* axis in the L*a*b*color space as described above, it is possible to enhance accuracy ininterpolating computation around the gray axis, which is performed whenthe color correction LUTs 610 and 620 are created with the use of thebase LUTs 510 and 520 after the smoothing processing. Accordingly, it ispossible to create the color correction LUTs 610 and 620 which areexcellent in color reproducibility and a gradation feature around thegray axis.

B-3. Processing Procedure for Smoothing Processing (Smoothing andOptimization Processing)

FIG. 13 is a flowchart showing a typical processing procedure of thesmoothing processing (Step S300 in FIG. 6). In Step T100, the initialvalue setting module 120 (FIG. 1) initially sets a plurality of latticepoints as targets of the smoothing processing.

FIG. 14 is a flowchart showing a detailed procedure of Step T100. InStep T102, a temporary ink amount for each lattice point as a target ofthe smoothing processing is determined based on the initial input valueof the ink amount (FIG. 7B, FIG. 9B). For example, in the smoothingprocessing for the 3D-LUT, the temporary ink amount I_((R,G,B)), withrespect to each input lattice point is determined based on the followingEquations (2) and (3).

$\begin{matrix}{I_{j{({R,G,B})}} = {{\left( {1 - r_{R}} \right)\left( {1 - r_{G}} \right)\left( {1 - r_{B}} \right)I_{j{({0,0,0})}}} + {\left( {1 - r_{R}} \right)\left( {1 - r_{G}} \right)r_{B}I_{j{({0,0,255})}}} + {\left( {1 - r_{R}} \right){r_{G}\left( {1 - r_{B}} \right)}I_{j{({0,255,0})}}} + {{r_{R}\left( {1 - r_{G}} \right)}\left( {1 - r_{B}} \right)I_{j{({255,0,0})}}} + {\left( {1 - r_{R}} \right)r_{G}r_{B}I_{j{({0,255,255})}}} + {{r_{R}\left( {1 - r_{G}} \right)}r_{B}I_{j{({255,0,255})}}} + {r_{R}{r_{G}\left( {1 - r_{B}} \right)}I_{j{({255,255,0})}}} + {r_{R}r_{G}r_{B}I_{j{({255,255,255})}}}}} & (2) \\{{r_{R} = \frac{R}{255}},{r_{G} = \frac{G}{255}},{r_{B} = \frac{B}{255}}} & (3)\end{matrix}$

Here, I_((R,G,B)) represents the entire ink amount I_(j) of the ink set(a combination of amounts of a plurality of kinds of ink) with respectto an RGB values at an input lattice point (an ink amount I_(j) of fourkinds of ink in the example shown in FIGS. 7A to 7C). An ink amount(temporary ink amount) with respect to an input lattice point in whichan RGB value is 0 or 255 is the initial input value input in advance bythe user in Step S200 in FIG. 6. According to the above Equations (2)and (3), it is possible to obtain a temporary ink amount I_((R,G,B)) atan arbitrary RGB value.

In the smoothing processing for the 4D-LUT, a temporary ink amountI_((C,M,Y,K)) with respect to each input lattice point is determinedbased on the following Equations (4) and (5).

$\begin{matrix}{I_{j{({C,M,Y,K})}} = {{\left( {1 - r_{C}} \right)\left( {1 - r_{M}} \right)\left( {1 - r_{Y}} \right)\left( {1 - r_{K}} \right)I_{j{({0,0,0,0})}}} + {\left( {1 - r_{C}} \right)\left( {1 - r_{M}} \right)\left( {1 - r_{Y}} \right)r_{K}I_{j{({0,0,0,255})}}} + {\left( {1 - r_{C}} \right)\left( {1 - r_{M}} \right){r_{Y}\left( {1 - r_{K}} \right)}I_{j{({0,0,255,0})}}} + {\left( {1 - r_{C}} \right){r_{M}\left( {1 - r_{Y}} \right)}\left( {1 - r_{K}} \right)I_{j{({0,255,0,0})}}} + {{r_{C}\left( {1 - r_{M}} \right)}\left( {1 - r_{Y}} \right)\left( {1 - r_{K}} \right)I_{j{({255,0,0,0})}}} + {\left( {1 - r_{C}} \right)\left( {1 - r_{M}} \right)r_{Y}r_{K}I_{j{({0,0,255,255})}}} + {\left( {1 - r_{C}} \right){r_{M}\left( {1 - r_{Y}} \right)}r_{K}I_{j{({0,255,0,255})}}} + {{r_{C}\left( {1 - r_{M}} \right)}\left( {1 - r_{Y}} \right)r_{K}I_{j{({255,0,0,255})}}} + {\left( {1 - r_{C}} \right)r_{M}{r_{Y}\left( {1 - r_{K}} \right)}I_{j{({0,255,255,0})}}} + {{r_{C}\left( {1 - r_{M}} \right)}{r_{Y}\left( {1 - r_{K}} \right)}I_{j{({255,0,255,0})}}} + {r_{C}{r_{M}\left( {1 - r_{Y}} \right)}\left( {1 - r_{K}} \right)I_{j{({255,255,0,0})}}} + {\left( {1 - r_{C}} \right)r_{M}r_{Y}r_{K}I_{j{({0,255,255,255})}}} + {r_{C}{r_{M}\left( {1 - r_{Y}} \right)}r_{K}I_{j{({255,255,0,255})}}} + {r_{C}r_{M}{r_{Y}\left( {1 - r_{K}} \right)}I_{j{({255,255,255,0})}}} + {{r_{C}\left( {1 - r_{M}} \right)}r_{Y}r_{K}I_{j{({255,0,255,255})}}} + {r_{C}r_{M}r_{Y}r_{K}I_{j{({255,255,255,255})}}}}} & (4) \\{\mspace{79mu} {{r_{C} = \frac{C}{255}},{r_{M} = \frac{M}{255}},{r_{Y} = \frac{Y}{255}},{r_{K} = \frac{K}{255}}}} & (5)\end{matrix}$

Since there are sixteen initial input values of the ink amounts for the4D-LUT as can be understood from Equation (4), setting of the initialinput values are complicated. Thus, a configuration is also applicablein which eight vertexes with K=0, that is eight vertexes including (C,M, Y, K)=(0, 0, 0, 0), (0, 0, 255, 0), (0, 255, 0, 0), (0, 255, 255, 0),(255, 0, 0, 0), (255, 0, 255, 0), (255, 255, 0, 0), and (255, 255, 255,0), and one vertex with k=255, for example a vertex of (C, M, Y, K)=(0,0, 0, 255) are regarded as input lattice points for which initial inputvalues of ink amounts are set and the ink amounts of the lattice pointwith K=255 are determined based on the following Equations (6) and (7).

I _((C,M,Y,255))=ƒ_(D1)(I _((C,M,Y,0)))+I _((0,0,0,255))  (6)

I _((C,M,Y,255))=ƒ_(D2)(I _((C,M,Y,0)) +I _((0,0,0,255)))  (7)

Here, I_((C,M,Y,255)) is an ink amount calculated based on the sameEquation as Equation (2) from the initial input values of the ink amountat eight vertexes with K=0. A function ƒ_(D1) in Equation (6) is afunction with which ink amount I_((C,M,Y,255)) is made to be within theduty limit value D_(I8) by reducing the entirety of the sum(I_((C,M,Y,0))+I_((0,0,0,255))) when the sum of the value I_((C,M,Y,0))and the value I_((0,0,0,255)) exceeds the duty limit value D_(I8). Inaddition, the function ƒ_(D2) in Equation (7) is a function with whichink amount I_((C,M,Y,255)) is made to be within the duty limit valueD_(I8) by reducing the entirety of the sumI_((C,M,Y,0))+I_((0,0,0,255))) when the sum of the value I_((C,M,Y,0))and the value I_((0,0,0,255)) exceeds the duty limit value D_(I8).

In Step T104 in FIG. 14, the hue values L*a*b* corresponding to thetemporary ink amounts are obtained with the use of the forward modelconverter 300. The computation can be expressed with the followingEquations (8) and (9).

L* _((R,G,B))=ƒ_(L*FM)(I _((R,G,B)))

a* _((R,G,B))=ƒ_(a*FM)(I _((R,G,B)))

b* _((R,G,B))=ƒ_(b*FM)(I _((R,G,B)))  (9)

L* _((C,M,Y,K))=ƒ_(L*FM)(I _((C,M,Y,K)))

a* _((C,M,Y,K))=ƒ_(a*FM)(I _((C,M,Y,K)))

b* _((C,M,Y,K))=ƒ_(b*FM)(I _((C,M,Y,K)))  (9)

Here, L*_((R,G,B)), a*_((R,G,B)), b*_((R,G,B)),L*_((C,M,Y,K),)a*_((C,M,Y,K)), and b*_((C,M,Y,K)) represent hue valuesL*a*b* after the conversion by the forward model, and the functionsƒ_(L*FM), ƒ_(a*FM), and ƒ_(b*FM) means conversion by the forward modelconverter 300. As can be understood from the equations, the hue valuesL*a*b* after the conversion are associated with the RGB values or theCMYU values as input values of the base LUT.

In Step T106 in FIG. 14, the hue values L*a*b* obtained in Step T104 areconverted again into the ink amounts with the use of the inverse modelinitial LUT 410. Here, the conversion into the ink amounts is performedagain with the use of the inverse model initial LUT 410 because theinitial input values of the ink amounts I_(j) and the temporary inkamounts determined in Step T102 are not always preferable ink amountsI_(j) as ink mounts for reproducing the L*a*b* values. On the otherhand, since preferable ink amounts in consideration of image quality andthe like are registered in the inverse model initial LUT 410, it ispossible to obtain preferable ink amount I_(j) for realizing the L*a*b*values as initial values by converting the L*a*b* values again into theink amounts I_(j) with the use of the inverse model initial LUT 410.However, Step T106 may be omitted. In Step T107, the aforementioned graytarget on the L* axis is set.

As a result of the aforementioned processing in Step T100, the followinginitial values are determined for the hue values as targets of thesmoothing processing.

(1) a value of an input lattice point in the base LUT: (R, G, B) or (C,M, Y, K)(2) an, initial coordinate value of a lattice point in the L*a*b* spacecorresponding to each input lattice point: (L*_((R,G,B)), a*_((R,G,B)),b*_((R,G,B))) or (L*_((C,M,Y,K)), a*_((C,M,Y,K)), b*_((C,M,Y,K)))(3) an initial ink amount corresponding to each input lattice point:I_((R,G,B)) or I_((C,M,Y,K))

As can be understood from the above description, the initial valuesetting module 120 has a function of setting initial values for theother input lattice points based on the input initial values for therepresentative input lattice points. In addition, the initial valuesetting module 120 may be included in the smoothing processing module130.

In Step T120 in FIG. 13, the color point displacement module 132displaces the hue values in the L*a*b* space based on the aforementioneddynamic model.

FIGS. 15A to 15D are explanatory diagrams showing processing contents inSteps T120 to T150 in FIG. 13. As shown in FIG. 15A, the distribution ofthe lattice points is significantly one-sided before the smoothingprocessing.

FIG. 15B shows a position of each lattice point after the elapse of ashort time. The L*a*b* value of each hue value after the displacementwill be described as a “target value “L*_(t)a*_(t)b*_(t) or LAB_(t)”.The modifying word “target” is used because the L*_(t)a*_(t)b*_(t) isused as a target value of an ink amount optimal value search processingwhich will be described later.

In Step T130, the ink amount optimization module 134 searches for anoptimal value for the ink amount I_(j) with respect to the target valueLAB_(t) with the use of a preset object function E (see FIG. 15C). Thatis, the ink amount is optimized (an optimal ink amount is searched for)with the use of the object function E for evaluating image quality whenthe amount I_(j) of ink designated as an amount with which the targetvalue LAB_(t) is substantially reproduced is made to adhere to themedium designated in Step S01, and the ink amount is determined. In theoptimization with the use of the object function E, the ink amountsI_(j) with which the L*a*b* value close to the coordinate values LAB_(t)of the hue values after the displacement by small amounts by the dynamicmodel are designated, and an ink amount with smaller sum of squareerrors of a plurality of parameters ΔL*, Δa*, ΔGI, ΔCII, ΔTI . . . isdetermined as an optimal ink amount I_(j) from among the designated inkamounts I_(j). In addition, the search for the optimal ink amount I_(j)is started from the initial ink amount of each input lattice point setin Step T100. Accordingly, the ink amount obtained in the search is avalue obtained by correcting the initial ink amount. The object functionE given in Equation (EQ1) can also be represented as a function in aquadratic form in relation to the ink amount vector I as Equation (EQ1),as will be described later. The optimization of the ink amount I_(j) isexecuted with the use of such an object function E in the quadratic formbased on a quadratic programming method. In addition, the detailedprocedure of Step T130 and the content of the object function E will bedescribed later.

In Step T140 in FIG. 13, the L*a*b* value corresponding to the inkamount (which has been determined to be an optimal value in previousStep T130) searched for in Step T130 is calculated again by the forwardmodel converter 300 (see FIG. 15D). Here, the L*a*b* value is calculatedagain because the L*a*b* value reproduced by the searched ink amountI_(j) which is an ink amount for minimizing the object function E, isslightly deviated from the target value LAB_(t) of the optimizationprocessing. The L*a*b* value calculated again as described above isemployed as a coordinate value of each lattice point after thedisplacement.

In Step T150, it is determined whether or not an average value(ΔLab)_(ave) of the displacement amounts of the hue values of thelattice points are a preset threshold value ε. The (ΔLab)_(ave) is anaverage value of the difference between the value before thedisplacement in Step T120 and the value after the calculation again inStep T140 for the hue value L*a*b* of each lattice point. When theaverage value (ΔLab)_(ave) is greater than the threshold value ε, theprocessing returns to Step T120, and the smoothing processing in StepsT120 to T150 is continued. On the other hand, the average value(ΔLab)_(ave) is equal to or less than the threshold value E, thedistribution of the hue values have been smoothed, and therefore, thesmoothing processing is completed. In addition, an appropriate value isexperimentally determined as the threshold value ε.

As described above, in the typical smoothing processing (smoothing andoptimization processing) according to the embodiment, each lattice pointis displaced by the dynamic model per short time, and an optimal inkamount I_(j) corresponding to the color point after the displacement issearched for by the optimization method. Then, such processing iscontinued until the displacement amount of the color point becomessufficiently small. As a result, it is possible to obtain a smoothlattice point distribution by the smoothing processing as shown in FIG.7C or FIG. 9C.

B-4. Content of Optimization Processing

The object function E (see FIG. 15C) of the optimization processing canbe expressed with the use of the hue value (L*a*b* value) as a functionof an ink amount and a Jacobian matrix J in relation to an image qualityevaluation index. Each image quality evaluation index is calculated bythe image quality evaluation index converter 136. Each image qualityevaluation index is an index for evaluating image quality when eachamount of ink is made to adhere to the basic medium, as will bedescribed later. The Jacobian matrix J is expressed by the followingEquation (10), for example.

$\begin{matrix}{J = \begin{pmatrix}\frac{\partial L^{*}}{\partial I_{1}} & \frac{\partial L^{*}}{\partial I_{2}} & \ldots & \frac{\partial L^{*}}{\partial I_{4}} \\\frac{\partial a^{*}}{\partial I_{1}} & \frac{\partial a^{*}}{\partial I_{2}} & \ldots & \frac{\partial a^{*}}{\partial I_{4}} \\\frac{\partial b^{*}}{\partial I_{1}} & \frac{\partial b^{*}}{\partial I_{2}} & \ldots & \frac{\partial b^{*}}{\partial I_{4}} \\\frac{\partial{GI}}{\partial I_{1}} & \frac{\partial{GI}}{\partial I_{2}} & \ldots & \frac{\partial{GI}}{\partial I_{4}} \\\frac{\partial{CII}_{A}}{\partial I_{1}} & \frac{\partial{CII}_{A}}{\partial I_{2}} & {\; \ldots} & \frac{\partial{CII}_{A}}{\partial I_{4}} \\\vdots & \vdots & \; & \vdots \\\frac{\partial{CII}_{F\; 12}}{\partial I_{1}} & \frac{\partial{CII}_{F\; 12}}{\partial I_{2}} & \ddots & \frac{\partial{CII}_{F\; 12}}{\partial I_{4}} \\\frac{\partial{GMI}}{\partial I_{1}} & \frac{\partial{GMI}}{\partial I_{2}} & \ddots & \frac{\partial{GMI}}{\partial I_{4}} \\\frac{\partial{TI}}{\partial I_{1}} & \frac{\partial{TI}}{\partial I_{2}} & \ldots & \frac{\partial{TI}}{\partial I_{4}}\end{pmatrix}} & (10)\end{matrix}$

The first to third rows in the right-hand side in Equation (10)represent values obtained by partially differentiating the hue valueL*a*b* with individual ink amounts I_(j). The rows from the fourth rowrepresent values obtained by partially differentiating an image qualityevaluation index (graininess index GI (Graininess Indexes), a colorinconstancy index CII (Color Inconstancy Index), a gamut evaluationindex GMI, and a total ink amount TI) representing image quality of acolor patch printed by a pair of ink amounts I_(j) (j=1 to 8), withindividual ink amounts I_(j). In addition, the image quality evaluationindexes GI, CII, GMI, TI are indexes which represent that the imagequality of the color patch reproduced by the ink amount I_(j) tends tobe better when the indexes are smaller.

The hue value L*a*b* is converted from the ink amount I_(j) with the useof the forward model converter 300 based on the following Equation (11).

L*=ƒ _(L*FM)(I)

a*=ƒ _(a*FM)(I)

b*=ƒ _(b*FM)(I)  (11)

The image quality evaluation indexes GI, CII, TI, and GMI can also berepresented as functions of ink amounts I_(j) (j=1 to 4) of a primarycolor in general.

$\begin{matrix}{\mspace{79mu} {{GI} = {f_{GI}(I)}}} & (12) \\{\mspace{79mu} {{CII}_{ill} = {f_{{CII}{({ill})}}(I)}}} & (13) \\{\mspace{79mu} {{TI} = {\sum\limits^{\;}I_{j}}}} & (14) \\{{GMI} = \sqrt{\left\{ {L_{GM}^{*} - {f_{L^{*}{FM}}(I)}} \right\}^{2} + \left\{ {a_{GM}^{*} - {f_{a^{*}{FM}}(I)}} \right\}^{2} + \left\{ {b_{GM}^{*} - {f_{b^{*}{FM}}(I)}} \right\}^{2}}} & (15)\end{matrix}$

In addition, the subscript “ill” of the color inconstancy indexCII_(ill) in Equation (13) represents a type of light source. In theaforementioned Equation (10), standard light A and standard light F12are used as types of the light sources. In addition, although an exampleof a calculation method of the color inconstancy index CII will bedescribed later, it is possible to use a color inconstancy index CIIrelating to one or a plurality of types of arbitrary standard lightsources can be used.

The graininess index GI can be calculated with the use of variousgraininess prediction model, and for example, it is possible tocalculate the index with the following Equation (16).

GI=a _(L)∫√{square root over (WS(u))}VTF(u)du  (16)

Here, aL represents a luminosity correction coefficient, WS(u)represents a Wiener spectrum of an image indicated by the halftone dataused in printing of the color patches, VTF(u) is a visual spatialfrequency feature, and u is a spatial frequency. The halftone data isdetermined by the halftone processing (which is the same as the halftoneprocessing executed by the printer 20) from the ink amounts I_(j) of thecolor patches. Although Equation (16) is expressed in a one-dimensionalmanner, it is easy to calculate a spatial frequency of a two-dimensionalimage as a function of a spatial frequency. As a method of calculatingthe graininess index GI, it is possible to use a method described inJP-A-2006-103640 disclosed by the present applicant, for example.According to the method described in JP-A-2006-103640, a graininessindex GI in the case of performing printing with an arbitrary ink amountby a neural network learned based on the graininess index GI obtained bymeasuring a color patch formed by causing a test ink amount I_(j) of inkis made to adhere. In this embodiment, a neural network is learned basedon a measurement result of a color patch formed on a basic medium.Substantially, the graininess index GI in the case of adhering theamount I_(j) of ink to the basic medium by the image quality evaluationindex converter 136 inputting an arbitrary ink amount I_(j) to theneural network.

The color inconstancy index CII is given by the following Equation (17),for example.

$\begin{matrix}{{CII} = \left\lbrack {\left( \frac{\Delta \; L^{*}}{2S_{L}} \right)^{2} + \left( \frac{\Delta \; C_{ab}^{*}}{2S_{C}} \right)^{2} + \left( \frac{\Delta \; H_{ab}^{*}}{S_{H}} \right)^{2}} \right\rbrack} & (17)\end{matrix}$

Here, ΔL* represents a luminosity difference in color patches under twodifferent observation conditions (under different light sources),ΔC*_(ab) represents a chromatic difference, and ΔH*_(ab) represents acolor phase difference. In the calculation of the color inconstancyindex CII, the L*a*b* values under two different observation conditionsare converted into values under a standard observation condition (underobservation with standard light D65, for example) with the use ofchromatic-adaption transform (CAT). In addition, since the L*a*b* valuesunder the observation conditions are calculated by the aforementionedforward model converter 300. Since the forward model converter 300(spectral printing model converter 310) is prepared for basic media, itis possible to evaluate color inconstancy in the case of causing eachamount I_(j) of ink to adhere the basic medium, with the colorinconstancy index CII. In relation to CII, see Billmeyer and Saltzman'sPrinciples of Color Technology, 3rd edition, John Wiley & Sons, Inc.,2000, p. 129, pp. 213-215.

The gamut evaluation index GMI is given by a color difference ΔE (CIE1976) between the hue value L*a*b* obtained by the forward modelconverter 300 and the target hue value L_(GM)*a_(GM)*b_(GM)*. The targethue value L_(GM)*a_(GM)*b_(GM)* is an outermost hue value in the L*a*b*color space. It is not necessary to consider gamut evaluation indexesGMI for all lattice points, and only lattice points on the vertexes, theridge lines, and the outer surfaces of the gamut may be taken intoconsideration. In addition, a target hue value L_(GM)*a_(GM)*b_(GM)*becomes different depending on each lattice point.

For example, if a hue value with the same color phase angle as that ofthe hue value L*a*b* obtained by the forward model converter 300 andwith higher chromaticity (the outermost of the L*a*b* color space) isset to the target hue value L_(GM)*a_(GM)*b_(GM)*, for example, it ispossible to evaluate whether or not the gamut becomes wide toward theside of high chromaticity. In addition, by setting a hue value on a graytarget to the target hue value L_(GM)*a_(GM)*b_(GM)* for the latticepoint corresponding to the gray axis lattice point, it is possible torestrict the lattice point to the gray target.

A component relating to the L* value among a plurality of components(also referred to as “elements”) of the Jacobian matrix J is given byEquation (18).

$\begin{matrix}{\frac{\partial L^{*}}{\partial I_{j}} = \frac{{f_{L^{*}{FM}}\left( {I + h} \right)} - {f_{L^{*}{FM}}(I)}}{h_{j}}} & (18)\end{matrix}$

Here, ƒ_(L*FM) represents conversion function from the ink amount I tothe L* value based on the forward model, I_(r) represents a currentvalue of the ink amount I, and h_(j) represents a small variation amountof j-th ink amount I_(j). Although Equation (17) was shown as an exampleof the L* value, the same is true for the a*b* value. Since the L*a*b*value is calculated by the aforementioned forward model converter 300(Equation (11)), the L*a*b* value means a hue value when each amountI_(j) of ink is made to adhere the basic medium. The other componentsexcept for the lowermost raw in the Jacobian matrix J are alsorepresented in the same form. If the element at the lowermost row in theJacobian matrix J is calculated based on Equations (14) and (18), allelements in the Jacobian matrix J become 1. This is because thevariation amount of the total ink amount TI when an ink amount I_(j) ofcertain ink is varied by a small variation amount h_(j) also becomesh_(j).

The object function E of the optimization is given by the followingEquation (19), for example.

$\begin{matrix}{E = {{w_{L^{*}}\left( {{\Delta \; L^{*}} - {\Delta \; L_{t}^{*}}} \right)}^{2} + {w_{a^{*}}\left( {{\Delta \; a^{*}} - {\Delta \; a_{t}^{*}}} \right)}^{2} + {w_{b^{*}}\left( {{\Delta \; b^{*}} - {\Delta \; b_{t}^{*}}} \right)}^{2} + {w_{GI}\left( {{\Delta \; {GI}} - {\Delta \; {GI}_{t}}} \right)}^{2} + {w_{{CII}{(A)}}\left( {{\Delta \; {CII}_{A}} - {\Delta \; {CII}_{A_{t}}}} \right)}^{2} + \ldots + {w_{{CII}{({F\; 12})}}\left( {{\Delta \; {CII}_{F\; 12t}} - {\Delta \; {CII}_{F\; 12t}}} \right)}^{2} + {w_{TI}\left( {{\Delta \; {TI}} - {\Delta \; {TI}_{t}}} \right)}^{2} + {w_{GMI}\left( {{\Delta \; {GMI}} - {\Delta \; {GMI}_{t}}} \right)}^{2}}} & (19)\end{matrix}$

Here, w_(L*), w_(a*), and the like described at the top of each term inthe right-hand side represents weight of each term. As the weightw_(L*), w_(a*) . . . of each term, the weight w_(L*), w_(a*) . . .designated by the user and stored on the setting table STB in Step S05is used. Particularly, when the user does not displace the positions ofthe pointers from the initial positions thereof, the default weightw_(L*), w_(a*) . . . is used. Accordingly, items valued by the objectfunction E depend on a medium and user setting.

The first term w_(L*)(ΔL*−ΔL*_(t))² in the right-hand side of Equation(19) is a square error relating to the variation amounts ΔL*, ΔL*_(t) ofthe hue value L*. The variation amounts ΔL*, ΔL*_(t) are given by thefollowing equation.

$\begin{matrix}{{\Delta \; L^{*}} = {{\sum\limits^{\;}{\frac{\partial L^{*}}{\partial I_{j}}\Delta \; I_{j}}} = {\sum\limits^{\;}{\frac{\partial L^{*}}{\partial I_{j}}\left( {I_{j} - I_{jr}} \right)}}}} & (20) \\{{\Delta \; L_{t}^{*}} = {L_{t}^{*} - {f_{L^{*}{FM}}\left( I_{r} \right)}}} & (21)\end{matrix}$

The partially differentiated value in the right-hand side of Equation(20) is a value given by the Jacobian matrix (Equation (10)), I_(j)represents an ink amount obtained as a result of the optimizationprocessing, and I_(jr) represents a current ink amount. The firstvariation amount ΔL* is an amount obtained by performing linearconversion on the variation amount ΔI_(j) of the ink amount by theoptimization processing with the partially differentiated value as acomponent of the Jacobian matrix. On the other hand, the secondvariation amount ΔL*_(t) is a difference between the target value L*_(t)obtained by the smoothing processing in Step T120 and the hue valueL*(I_(r)) given by the current ink amount I_(r). In addition, it ispossible to regard the second variation amount ΔL*_(t) as a differenceof the L* values before and after the smoothing processing.

Each item from the second item on the right-hand side of Equation (19)is also given by the similar equation as Equations (20) and (21). Thatis, the object functions E are given as sums of square errors betweenthe first variation amounts ΔL*, Δa*, Δb*, ΔGI . . . obtained byperforming linear conversion on the ink amount variation amount ΔI_(j)by the optimization processing with the components of the Jacobianmatrix and the second variation amounts ΔL*_(t), Δa*_(t), Δb*_(t),ΔGI_(t) . . . before and after the smoothing processing in relation tothe parameters L*, a*, b*, GI . . . .

Incidentally, the first variation amounts ΔL*, Δa*, Δb*, ΔGI . . . canbe expressed in the forms of the following Equations (22) and (23) withthe use of a matrix.

$\begin{matrix}{\begin{pmatrix}{\Delta \; L^{*}} \\{\Delta \; a^{*}} \\{\Delta \; b^{*}} \\{\Delta \; {GI}} \\{\Delta \; {CII}_{A}} \\\vdots \\{\Delta \; {CII}_{F\; 12}} \\{\Delta \; {GMI}} \\{\Delta \; {TI}}\end{pmatrix} = {{J \cdot \Delta}\; I}} & (22) \\{{\Delta \; I} = {{I - I_{r}} = \begin{pmatrix}{\Delta \; I_{1}} \\{\Delta \; I_{2}} \\\vdots \\{\Delta \; I_{4}}\end{pmatrix}}} & (23)\end{matrix}$

In addition, Equation (19) can be described as Equation (24) with theuse of a matrix.

$\begin{matrix}\begin{matrix}{E = {\left( {{J\left( {I - I_{r}} \right)} - {\Delta \; M}} \right)^{T}{W_{M}\left( {{J\left( {I - I_{r}} \right)} - {\Delta \; M}} \right)}}} \\{= {\left( {{I^{T}J^{T}} - \left( {{I_{r}^{T}J^{T}} + {\Delta \; M^{T}}} \right)} \right){W_{M}\left( {{JI} - \left( {{JI}_{r} + {\Delta \; M}} \right)} \right)}}} \\{= {{I^{T}J^{T}W_{M}{JI}} - {2\left( {{I_{r}^{T}J^{T}} + {\Delta \; M^{T}}} \right)W_{M}{JI}} +}} \\{{\left( {{I_{r}^{T}J^{T}} + {\Delta \; M^{T}}} \right){W_{M}\left( {{JI}_{r} + {\Delta \; M}} \right)}}}\end{matrix} & (24)\end{matrix}$

Here, T represents transposition of a matrix. The matrix W_(M) is adiagonal matrix in which weight is arranged at each of the diagonalelements (see Equation (25)), and the matrix ΔM is a target variationamount vector relating to each parameter (see Equation (26)).

$\begin{matrix}{W_{M} = \begin{pmatrix}w_{L^{*}} & 0 & \; & \; & \ldots & \; & \; & 0 \\\; & w_{a^{*}} & \; & \; & \; & \; & \; & \; \\\; & \; & w_{b^{*}} & \; & \; & \; & \; & \; \\\; & \; & \; & w_{GI} & \; & \; & \; & \vdots \\\vdots & \; & \; & \; & \ddots & \; & \; & \; \\\; & \; & \; & \; & \; & w_{{CII}{({F\; 12})}} & \; & \; \\\; & \; & \; & \; & \; & \; & w_{GMI} & 0 \\0 & \; & \; & \ldots & \; & \; & 0 & w_{TI}\end{pmatrix}} & (25) \\{{\Delta \; M} = {\begin{pmatrix}{\Delta \; L_{t}^{*}} \\{\Delta \; a_{t}^{*}} \\{\Delta \; b_{t}^{*}} \\{\Delta \; {GI}_{t}} \\{\Delta \; {CII}_{At}} \\\vdots \\{\Delta \; {CII}_{F\; 12t}} \\{\Delta \; {GMI}_{t}} \\{\Delta \; {TI}_{t}}\end{pmatrix} = {\begin{pmatrix}{L_{t}^{*} - {f_{L^{*}{FM}}\left( I_{r} \right)}} \\{a_{t}^{*} - {f_{a^{*}{FM}}\left( I_{r} \right)}} \\{b_{t}^{*} - {f_{b^{*}{FM}}\left( I_{r} \right)}} \\{{GI}_{t} - {{GI}\left( I_{r} \right)}} \\{{CII}_{At} - {{CII}_{A}\left( I_{r} \right)}} \\\vdots \\{{CII}_{F\; 12t} - {{CII}_{F\; 12}\left( I_{r} \right)}} \\{{GMI}_{t} - {{GMI}\left( I_{r} \right)}} \\{{TI}_{t} - {\sum\limits^{\;}I_{jr}}}\end{pmatrix} = {{const}.}}}} & (26)\end{matrix}$

The right-hand side in Equation (26) is a difference between the targetvalue relating to each of the parameters L*, a*, b*, CII . . . (alsoreferred to as “elements”) and each parameter value given by the currentink amount I_(r). Among the target values of the parameters, the huevalue L*_(t), a*_(t), b*_(t) is determined by the smoothing processing(Step T120). There are some methods for determining the target variationamounts ΔGI_(t), ΔCII_(t), ΔTI_(t), and ΔGMI_(t) obtained from thetarget value of the image quality evaluation index and the currentquality image quality evaluation index. A first method is a method usingpredetermined constants (for example, ΔGI_(t)=−2, ΔCII_(t)=−1,ΔTI_(t)=−1, ΔGMI_(t)=−1) are used as the target variation amountsΔGI_(t), ΔCII_(t), ΔTI_(t), and ΔGMI_(t). In addition, negative valuesare used as constants because the image quality evaluation indexes areindexes which indicate higher image quality the smaller they are. Inaddition, it is preferable to set the target value GI_(t) of thegraininess index GI to zero. A second method is a method in which thetarget values GI_(t), CII_(t), TI_(t), and ΔGMI_(t) are defined asfunctions of the target values L*_(t), a*_(t), b*_(t) of the hue values.Since the target value of each parameter is determined before theoptimization processing as described above, all the components of thetarget variation amount vector ΔM are constants.

The third term (I_(r) ^(T)J^(T)+ΔM^(T)) W_(M) (JI_(r)+ΔM) among theterms in the right-hand side of Equation (24) is a constant since thethird term does not include the ink amount I obtained as a result of theoptimization. In general, a constant term is not necessary in the objectfunction E for optimization. Thus, if constant terms are deleted fromEquation (24), and the entirety is multiplied by ½, the followingEquation (27) is obtained.

E=½I ^(T) J ^(T) W _(M) JI−(I _(r) ^(T) J ^(T) +ΔM ^(T))W _(M) JI  (27)

Here, if a matrix A and a vector g are defined as the followingEquations (28) and (29), Equation (27) can be expresses as Equation(30).

A=J ^(T) W _(M) J  (28)

g=(I _(r) ^(T) J ^(T) +ΔM ^(T))W _(M) J  (29)

E=½I ^(T) AI−gI  (30)

The object function E given by Equation (30) can be understood to be ina quadratic form relating to the ink amount vector I obtained by theoptimization. Equations (EQ1) and (EQ2) shown in FIG. 15C are same asEquations (19) and (30), respectively.

Since the object function E in the secondary form as in Equation (30) isused in the optimization processing of this embodiment, it is possibleto use a secondary planning method as an optimization method. Here, the“quadratic programming method” means a narrowly defined quadraticprogramming method which does not include a sequential quadraticprogramming method. If a quadratic programming method with the use of anobject function in a quadratic form is used, it is possible tonoticeably speed up the processing as compared with a case in whichanother non-linear programming method such as a quasi-Newton method, asequential quadratic programming method, or the like is used.

Incidentally, the search for the ink amount by the optimizationprocessing according to this embodiment is executed under the followingconditions.

(Optimization condition) the object function E is to be minimized.(Restriction condition) the duty limit value is to be satisfied.

In the case of a basic medium, the hue limit value D_(Ij) stored on thesetting table STB in Step S08 is used as it is as the duty limit value.In addition, the image quality evaluation index converter 136 and theforward model converter 300 (spectral printing model converter 310) canpredict a hue value, an image quality evaluation index GI, and the likefor the ink amount I_(j) which satisfies the duty limit value D_(Ij).

The restriction condition relating to the duty limit value can beexpressed by the following Equation (31).

b ^(T) I=(1 0 . . . 0)I≦D _(I)  (31)

Here, the vector b is a coefficient for identifying an ink type as atarget of the duty limit value and is a vector with 0 or 1 as anelement. For example, in the case of a duty limit value relating to onetype of ink, only one element of the vector b becomes 1. On the otherhand, in the case of a duty limit value relating to the total inkamounts for all types of ink, all elements of the vector b become 1. Drin the right-hand side of Equation (31) is a vector including individualduty limit values D_(Ij) as elements. It is assumed that j=1 to 8 issatisfied both in the right-hand side and in the left-hand side ofEquation (31). That is, the total ink amounts I₅ to I₇ for the secondarycolor and the total ink amount I₈ are also taken into consideration inorder to impose the restriction condition in relation to the duty limitvalues.

There is also restriction that each ink amount I_(j) (j=1 to 8) is not anegative value. The restriction that the ink amount is not a negativevalue can be expressed by the following Equation (32).

b _(nz) ^(T) I=(1 0 . . . 0)I≧0  (32)

If Equations (31) and (32) are combined, the duty limit value can begiven by the following Equation (33).

$\begin{matrix}{{BI} = {{\begin{pmatrix}1 & 0 & \ldots & 0 \\0 & 1 & \; & \vdots \\\vdots & \; & \ddots & 0 \\0 & \ldots & 0 & 1 \\\; & \; & \; & \; \\{- 1} & 0 & \ldots & 0 \\0 & {- 1} & \; & \vdots \\\vdots & \; & \ddots & 0 \\0 & \ldots & 0 & {- 1}\end{pmatrix}I} \leq \begin{pmatrix}D_{I\; 1} \\\vdots \\\vdots \\D_{I\; 8} \\\; \\0 \\\vdots \\\vdots \\0\end{pmatrix}}} & (33)\end{matrix}$

The restriction expressed by Equation (33) is linear inequality signrestriction. In general, the quadratic programming method can beexecuted under linear restriction. That is, according to theoptimization processing of this embodiment, an optimal ink amount issearched for by executing the quadratic programming method with the useof an object function in a quadratic form given by Equation (30) underthe restriction of Equation (33). As a result, it is possible tostrictly satisfy the linear restriction and execute the ink amountsearch at a high speed.

FIG. 16 is a flowchart showing a detailed procedure of the optimizationprocessing (Step T130 in FIG. 13). In Step T132, a target variationamount ΔM given by Equation (26) is firstly obtained. The targetvariation amount ΔM is determined based on the target value L*_(t),a*_(t), b*_(t) obtained in Step T120 (smoothing processing), the currentink amount I_(r), and the like as described above.

In Step T134, a Jacobian matrix J given by Equation (10) is calculated.In addition, each component of the Jacobian matrix J is a valuecalculated in relation to the current ink amount I_(r) (a value beforethe smoothing and the optimization) as expressed by Equation (18) as anexample.

In Step T136, optimization of the ink amount I_(j) is executed so as tominimize a difference between a result ΔL*, Δa*, Δb*, ΔGI . . . of thelinear conversion by the Jacobian matrix J and the target variationamount ΔM (ΔL*_(t), Δa*_(t), Δb*_(t), ΔGI_(t) . . . ) (determine an inkamount set to minimize the object function W among a plurality of inkamount sets (one ink amount set is configured by I₁, I₂, I₃, I₄) whichreproduces L*, a*, b* around the target value LAB_(t) and satisfies theduty limit value). This optimization is realized by executing thequadratic programming method with the use of the object function E inthe quadratic form given by Equation (30). Since the ink amount I_(j) isoptimized under the restriction by the duty limit value D_(Ij) stored onthe setting table STB in Step S08 as described above, optimizationresults are differently obtained in accordance with the media. Inparticular, the sizes of the gamut greatly depend on the duty limitvalue D_(Ij) and become different in accordance with the media. It is amatter of course that the prediction results of the hue values, imagequality evaluation indexes GI, and the like by the image qualityevaluation index converter 136 and the forward model converter 300 arealso different depending on the media, and therefore, optimizationresults of the ink amount I_(j) are differently obtained.

As described above with reference to the flowchart in FIG. 13, when itis determined that convergence is insufficient after the optimizationprocessing in Step T130 (“No” in Step T150), the smoothing (Step T120)and the optimization processing (Step T130) are executed again. At thistime, as initial values for the smoothing and the optimizationprocessing, values obtained in the previous smoothing and optimizationprocessing are used. In addition, it is not necessary to repeat theprocessing, and the smoothing and the optimization processing may beperformed at least once.

C. CONFIGURATION OF PRINTING APPARATUS

FIG. 17 shows a configuration of the printer 20. In the drawing, theprinter 20 is provided with a CPU 50, a RAM 52, a ROM 51, a memory cardslot 53, a bus 54, and an ASIC 55. By the CPU 50 developing the programdata 15 a, which is stored on the ROM 51, on the RAM 52 and performingcomputation based on the program data 15 a, firmware FW for controllingthe printer 20 is executed. The firmware FW can create drive data basedon print data PD stored on a memory card MC mounted on the memory cardslot 53. The ASIC 55 obtains the drive data and generates drive signalsfor a paper feeding mechanism 57, a carriage motor 58, and a print head59. On the ROM 51, the color correction 3D-LUT 610 provided from thecomputer 10 is stored. The setting table STB is attached to the colorcorrection 3D-LUT 610, and the color correction 3D-LUT 610 is preparedfor each medium described in the setting table STB. The printer 20 isprovided with a carriage 60, and the carriage 60 is provided withcartridge holders 61 a to which a plurality of ink cartridges 61 can beattached. The carriage 60 is provided with a print head 59 whichdischarges ink of each color of CMYK respectively provided from the inkcartridges 61.

FIG. 18 shows a software configuration of the firmware FW. The firmwareFW is configured by an image data obtaining unit FW1, a rendering unitFW2, a color conversion unit FW3, a halftone unit FW4, and a rasterizingunit FW5. The image data obtaining unit FW1 obtains the print data PD,which is stored on the memory card MC, as a print target. The print dataPD may be document data, graphic data, or a picture image data. Therendering unit FW2 generates input image data ID used for printing basedon the print data PD. The input image data ID is configured by pixels,the number of which (printing resolution×actual printing size)corresponds to the printing resolution (2880×2880 dpi, for example), andeach pixel is expressed by an RGB value based on the CIE-sRGB colorspace of eight bits (0 to 255).

The color conversion unit FW3 obtains the input image data ID andperforms color conversion on the input image data ID. Specifically, thecolor conversion unit FW3 converts the RGB value into an ink amountI_(j) of each kind of ink by executing interpolating computation withreference to the color correction 3D-LUT 610. Although the colorcorrection 3D-LUT 610 is prepared for each medium, it is not possible toexecute printing on a medium when the medium for which the correspondingcolor correction 3D-LUT 610 is not stored is set or designated in theprinter 20. The halftone unit FW4 executes halftone processing based onthe ink amount I_(j) of each kind of ink output by the color conversionunit FW3. The rasterizing unit FW5 allots each pixel (dischargeavailability) of halftone data after the halftone processing to eachmain scanning and each ink nozzle of the print head 59 to generate drivedata. The drive data is output to the ASIC 55, and the ASIC 55 generatesdrive signals for the paper feeding mechanism 57, the carriage motor 58,and the print head 59. Although the color conversion processing isperformed by the firmware FW on the printer 20 according to thisembodiment, the color conversion processing may be performed on acomputer to which the printer 20 is connected. That is, the colorcorrection 3D-LUT 610 may be installed in a computer (print controlapparatus) which controls the printer 20, as well as in the printer 20.

As described above, it is not possible to execute printing on a mediumfor which the corresponding color correction 3D-LUT 610 is not stored.This is because the forward model converter 300 and the image qualityevaluation index converter 136 used in creating the color correction3D-LUT 610 are prepared for a certain medium (basic medium) as a targetand it is not possible to realize a desired reproduced color and imagequality even if the color correction 3D-LUT 610 is used for anothermedium. Ideally, it is necessary to prepare the color correction 3D-LUTs610 for all printing media. That is, it is necessary to performprocessing for creating the color correction 3D-LUT 610 for all kinds ofprinting media based on the aforementioned procedure. However, since itis necessary to form multiple color patches on each medium and performmeasurement in order to prepare (generate) the forward model converter300 and the image quality evaluation index converter 136, it isdifficult to prepare the forward model converter 300 and the imagequality evaluation index converter 136 for all kinds of media. To beginwith, it is not possible to prepare, the forward model converter 300 andthe image quality evaluation index converter 136 for unknown media.Thus, an embodiment of the invention provides a method for creating anLUT for diverting media which are different from the basic media bydiverting the forward model converter 300 and the image qualityevaluation index converter 136 prepared for limited media (basic media)without preparing the forward model converter 300 and the image qualityevaluation index converter 136 for each medium. Hereinafter, descriptionwill be given of the procedure.

D. DIVERTING MEDIA LUT CREATION PROCEDURE

In Step S06 in the overall processing in FIG. 2, the computer 10executes processing from Step S09 when it is determined that a divertingmedium has been designated. First, in Step S09, the LUT creationcondition setting module 700 determines a diverted medium. The divertedmedium means a basic medium which belongs to the same group as that ofthe diverting medium designated in Step S01 among the basic media. Whenthe group of the designated diverting medium is unclassified, a basicmedium in which each kind of ink has a standard color forming feature isdetermined to be the diverted medium among the basic media. Informationfor specifying the diverted medium is registered in the setting tableSTB by the setting information storage module 730. In Step S10, thesetting information storage module 730 obtains color forming featuredata and the duty limit value D_(Ij) of the diverted medium stored onthe medium table MTB (hereinafter, the duty limit value D_(Ij) of thediverted medium will be described as a standard duty limit valueD_(SIj)) and registers the standard duty limit value D_(SIj) in thesetting table STB.

In Step S11, the LUT creation condition setting module 700 prints colorpatches for evaluating the color forming feature (hue value feature) ofthe medium on the designated diverting medium. Specifically, the LUTcreation condition setting module 700 generates patch image data forprinting color patches and outputs the patch image data to the halftoneunit FW4 of the printer 20. The patch image data is image data, in whicheach pixel has an ink amount I_(j) (j=1 to 4), which is for printingcolor patches based on gradation of the ink amounts I_(j) (j=1 to 8) ofprimary colors of ink (C, M, Y, K), secondary colors (R, G, B), and acolor obtained by mixing all ink. For example, the individual inkamounts I_(j) (j=1 to 4) in gradation of the secondary colors and allthe kinds of ink are uniform. A character which represents the inkamount I_(j) (j=1 to 8) used in printing of a color patch is added toeach color patch. In Step S12, color measurement is performed by acolorimeter on each color patch printed on the diverting medium by theprinter 20, and the computer 10 obtains the color measurement value(CIE-L*a*b* color system). In Step S13, the UI module 720 causes adisplay apparatus to display a medium feature designation UI image fordesignating a color forming feature of the diverting medium.

FIG. 19 is a diagram showing an example of the medium featuredesignation UI image. In the drawing, color measurement values (huevalues) obtained by performing color measurement on the color patches(only of C, M, Y, and K) of gradation are shown by graphs as examples.In the graphs for the chromatic color patches (C, M, and Y), thevertical axis represents chromaticity C*. In the graph for theachromatic color patch (K), the vertical axis represents luminosity L*.The horizontal axis represents an ink amount I_(j) (j=1 to 8). In eachgraph, the chromatic ness or the brightness based on the measurementvalue of each color patch printed in Step S11 is plotted (white circles)corresponding to a plurality of reference points (ink amounts of eachcolor patch). In so doing, the color forming features in accordance withthe ink amounts I_(j) (j=1 to 8) in the diverting medium are representedin the graphs. In addition, the color forming feature of the divertedmedium obtained from the medium table MTB is also plotted (blackcircles) so as to be comparable in each graph. That is, the same colorpatches are printed and subjected to color measurement in advance evenfor the diverted medium (basic medium), and the color measurement resultcorresponding to the ink amount of each color patch is stored on themedium table MTB as color forming feature data.

In the medium feature designation UI image, text boxes are provided intowhich the user inputs as duty limit values D_(Ij) the ink amounts I_(j)(j=1 to 8) described in the color patches where ink bleeding starts tooccur as a result of user's observation on the color patches of theprimary colors of ink (C, M, Y, K), the secondary colors (R, G, B), andall kinds of ink. The LUT creation condition setting module 700 maydetermine the ink amounts I_(j) (j=1 to 8) from which the colormeasurement values become unstable due to ink bleeding or the like andregard the ink amounts as the duly limit values D_(Ij) without dependingon the user's observation. In the medium feature designation UI image, aduty limit value enter button is provided, and the setting informationstorage module 730 obtains the input duty limit value D_(Ij) (Step S14)when the button is clicked, and stores the duty limit value D_(Ij) onthe setting table STB (Step S15). As described above, the duty limitvalue D_(Ij) can be set for the diverting medium, the duty limit valueD_(Ij) of which has not been known. In addition, in the followingdescription of “D. Diverting media LUT creation procedure”, D_(Ij)indicates the duty limit value D_(Ij) for the diverting mediumdesignated in Step S01 as long as there is no particular mention.

In Step S16, the LUT creation condition setting module 700 normalizes ahue value feature (first hue value feature) indicating a variation ofthe hue value in the diverted medium corresponding to the variation inink amounts up to the standard duty limit value D_(SIj) for the divertedmedium and a hue value feature (second hue value feature) indicating avariation of a hue value in the diverting medium corresponding to avariation in ink amounts up to the duty limit value D_(Ij) for thediverting medium.

FIG. 20A shows an example of the two hue value features before thenormalization, and FIG. 20B shows an example of the two hue valuefeatures after the normalization. In FIGS. 20A to 20C (and FIGS. 21A to21C), the first hue value feature is shown by solid lines, and thesecond hue value feature is shown by chain lines. Here, as the first huevalue feature and the second hue value feature, features of theluminosity L* with respect to the K ink (ink (luminosity amount I₄)^((luminosity) feature) is employed. That is, the two graphs shown inFIG. 20A correspond to the two graphs for the color patch (K) shown asan example in FIG. 19 (it is a matter of course that each drawing showsjust an example and the contents of the graphs do not coincide with eachother). The specific method for normalization is not particularlylimited, and the ink amount range (0 to D_(I4)) of the second hue valuefeature may be normalized with reference to the first hue value featureby multiplying the ink amount I_(j) of the second hue value feature bythe ratio (D_(SI4)/D_(I4)) of the reference duty limit value D_(SIj)with respect to the duty limit value D_(Ij). Alternatively, the inkamount range (0 to D_(SI4)) of the first hue value feature and the inkamount range (0 to D_(I4)) of the second hue value feature arerespectively normalized to predetermined numerical value ranges (0 to1.0, for example). In FIG. 20B, the latter method is used to performnormalization.

That is, in FIG. 20B, the ink amount range of the first hue valuefeature is normalized by multiplying the ink amount I₄ indicating aposition of the plotting of the color measurement value for the colorpatch (K) printed on the diverted medium in the vertical direction bythe normalization ratio 1/D_(SI4 for the) first hue value feature, andthe ink amount rage of the second hue value feature is normalized bymultiplying the ink amount I₄ indicating _(a) position of the plottingof the color measurement value for the color patch (K) printed on thediverting medium in the horizontal direction by the normalization ratio1/D_(I4) for the second hue value feature. In FIGS. 20A to 20C (andFIGS. 21A to 21C), the luminosity of the vertical axis is shown in astate normalized to 0 to 100. The processing in Steps S10 to S16includes the first obtaining step and the second obtaining stepaccording to an embodiment of the invention.

In Step S17, the LUT creation condition setting module 700 performsprocessing for correcting and approximating the second hue value featureto the first hue value feature. FIG. 20C shows an example of a state inwhich the second hue value feature after the normalization isapproximated to the first hue value feature hue value feature after thenormalization. As specific processing in Step S17, the LUT creationcondition setting module 700 displaces a position of a maximum valueD_(max)(=1.0) of the ink amount in the second hue value feature (FIG.20B) after the normalization along the horizontal axis and alsodisplaces positions of the other reference points in the second huevalue feature after the normalization in the horizontal axis along withthe displacement of the maximum value D_(max). The displacementdirections and the position variation n rates before and after thedisplacement are the same both for the maximum value and for the otherreference points. In the case where the second hue value feature is afeature according to which higher luminosity is defined as a whole thanthe first hue value feature as shown in FIG. 20B, the maximum valueD_(max) is displaced in a direction in which the value thereof isreduced. On the other hand, in the case where the second hue valuefeature is a feature according to which lower luminosity is defined as awhole than the first hue value feature, the maximum value D_(max) isdisplaced in a direction in which the value thereof is increased.

The LUT creation condition setting module 700 calculates an approximatecurve based on the maximum value D_(max a)nd the other reference pointsafter the displacement as described above by a least-square method orthe like and regards the calculated approximate curve as a candidate ofthe second hue value feature after the correction. The LUT creationcondition setting module 700 evaluates a degree of approximation betweenthe approximate curve which is thus generated as a candidate as thefirst hue value feature after the normalization. Such generation of anapproximate curve and evaluation of a degree of approximation betweenthe approximate curve and the first hue value feature are repeatedmultiple times while the displacement amounts of the maximum valueD_(max) (and the other reference points) are changed, and an approximatecurve with the highest degree of approximation in the repetition isfixed as the second hue value feature (FIG. 20C) after the correction.Although there are various evaluation methods of the degree of theapproximation, an approximate curve according to which a minimum squareerror can be obtained for a predetermined reference point on the firsthue value feature and a predetermined reference point on the approximatecurve is evaluated as an approximate curve with the highest degree ofapproximation.

In addition, the LUT creation condition setting module 700 may evaluatethe degree of the approximation between the approximate curve and thefirst hue value feature while giving more weight on evaluation toreference points belonging to a specific hue value range among aplurality of reference points on the approximate curve than the otherreference points at the time of the evaluation of the degree of theapproximation. More specifically, evaluation is performed after givingmore weight on reference points belonging to a specific intermediateluminosity region (for example, a region including luminosity L*=30 to70) from among a plurality of reference points on the approximate curvethan the other reference points.

In Step S18, the LUT creation condition setting module 700 regards avalue indicated by the maximum value D_(max)′ in the fixed second huevalue feature after the correction as a revision value RW for the dutylimit value. Since the second hue value feature is approximated to thefirst hue value feature by displacing the maximum value D_(max) in adirection in which the value thereof is decreased in the example shownin FIGS. 20B and 20C, the maximum value D_(max)′ is a value which issmaller than the maximum value 1.0 of the ink amount in the first huevalue feature. That is, the revision value RW represents a ratio withrespect to the maximum value (standard duty limit value D_(SIj)) of theink amount in the first hue value feature. The revision value RW withrespect to the duty limit value here is a value for determining a dutylimit value (a new limit value in an embodiment of the invention) to besatisfied when optimization of the ink amount is executed (as will bedescribed later) with the use of the forward model converter 300 and theimage quality evaluation index converter 136 prepared for the divertedmedium in order to create a base LUT for medium (diverting medium) forwhich the forward model converter 300 and the image quality evaluationindex converter 136 are not prepared. The LUT creation condition settingmodule 700 stores the obtained revision value RW on the setting tableSTB.

FIGS. 21A to 21C are an example showing a relationship between the firsthue value feature (solid line) and the second hue value feature and astate in which the first hue feature value and the second hue featurevalue are normalized (Step S16) and approximated (Step S17), which is anexample different from that in FIGS. 20A to 20C. In the example shown inFIGS. 20A to 20C, the second hue value feature is a feature according towhich a higher luminosity is defined as a whole than the first hue value(FIG. 20B). However, in the example shown in FIGS. 21A to 21C, thesecond hue value feature is a feature according to which lowerluminosity is defined as a whole than the first hue value feature (FIG.20B). Therefore, when the second hue value feature is corrected andapproximated to the first hue value feature in Step S17 as describedabove in the example in FIGS. 21A to 21C, a value (revision value RW)indicated by the maximum value D_(max)′ in the second hue value feature(FIG. 21C) after the correction becomes a value which is greater thanthe maximum value 1.0 of the ink amount in the first hue value feature.

In Step S19, the LUT creation condition setting module 700 defines aconversion relationship of the ink amount based on the first hue valuefeature and the second hue value feature. The conversion relationshiphere is a conversion relationship for converting the ink amountdetermined by executing the ink amount optimization with the use of theforward model converter 300 and the image quality evaluation indexconverter 136 prepared for the diverted medium into an ink amount whichcan be applied to the feature of the diverting medium in order togenerate the base LUTs 510 and 520 for the diverting medium. That is,the ink amount determined by the optimization with the use of theforward model converter 300 and the image quality evaluation indexconverter 136 prepared for the diverted medium is an optimal ink amountfor reproducing a certain hue value on the diverted medium, andtherefore, it is necessary to convert the ink amount into an ink amountwhich can reproduce the same hue value on the diverting medium, and aconversion relationship therefor is defined.

In such a case, the LUT creation condition setting module 700 calculatesa nonlinear conversion function (for example, a γ curve) so as toconvert the ink amounts I_(j) corresponding to (a single or a pluralityof) hue values in the first hue value feature into ink amounts I_(j)corresponding to the same or approximate hue values in the second huevalue feature, as an example of the conversion relationship. Forexample, as shown in FIG. 20A as an example, a nonlinear functionƒ_(CVj) so as to convert the ink amount I_(4m) which reproduces certainluminosity L*=50 on the diverted medium (the first hue value feature)into the ink amount L_(4m)′ which reproduces the luminosity L*=50 in thediverting medium (second hue value feature). In addition, the nonlinearfunction ƒ_(CVj) may have a conversion feature of converting the inkamount I₄ corresponding at least to the standard duty limit valueD_(SI4) ×RW into the ink amount I₄ reproducing the luminosity L*, towhich the ink amount corresponds in the diverted medium (first hue valuefeature), in the diverting medium (second hue value feature).

Alternatively, the LUT creation condition setting module 700 maygenerate an LUT in which the ink amounts of the first hue value featureand the ink amount in the second hue value feature are associated witheach other for the common hue values and regards the LUT as theconversion relationship instead of the nonlinear function ƒ_(CVj). Eventhrough such an LUT, it is possible to convert the ink amount I_(j)corresponding to the hue value in the first hue value feature into theink amount I_(j) corresponding to the same hue value in the second huevalue feature. Although the description was given of examples of the Kink with reference to FIGS. 20A to 21C, a nonlinear function ƒ_(CVj) oran LUT with a feature of converting the ink amount I_(j) whichreproduces predetermined chromaticities C* on the diverted medium (firsthue value feature) into the ink amount which reproduces thechromaticities on the diverting medium (second hue value feature) isgenerated for each of the other chromatic ink (C, M, Y) as well as aconversion relationship for the chromatic ink.

In Step S20, the conversion relationship for each primary color inkdefined in Step S19 is set in the ink amount converter 710. In so doing,the ink amount converter 710 can convert the ink amount I_(j) (j=1 to 4)based on the conversion relationship.

In Step S21, a*, b* values when the CMY ink is made to separately adhereto the diverting medium up to the duty limit value D_(Ij) (j=1 to 3)(hereinafter, described as diverting medium tone (a_(cj)*, b_(cj)*) (j=1to 3)) and a*, b* values when the CMY ink is made to separately adhereto the diverted medium up to the standard duty limit value D_(Ij) (j=1to 3) (hereinafter, described as diverted medium tone (a_(sj)*, b_(sj)*)(j=1 to 3)) are obtained and analyzed. Such hue values are obtained ascolor measurement values obtained from the color patches correspondingto the duty limit value D_(Ij) (j=1 to 3) and the standard duty limitvalue D_(SIj) (j=1 to 3) in Steps S10 and S12. The diverting medium tone(a_(Cj)*, b_(Cj)*) and the diverted medium tone (a_(Sj)*, b_(Sj)*) maybe obtained from color patches in which predetermined luminosity L andchromaticities C* are reproduced or may be obtained from color patchesbased on a predetermined ink amount (for example, 15% or the like withrespect to the duty limit value D_(Ij), D_(SIj)) other than the dutylimit value D_(Ij), D_(SIj). Furthermore, the diverting medium tone(a_(Cj)*, b_(Cj)*) and the diverted medium tone (a_(Sj)*, b_(Sj)*) maybe obtained from color patches of composite gray formed by causing theamount I_(j) (j=1 to 3) of ink to adhere to each medium by an equalamount. In any case, not the hue values of each medium itself but thehue values of each medium in a state in which ink adheres to some extentare obtained, and therefore, it is possible to evaluate the tone of anintermediate luminosity region.

FIG. 22 is a graph obtained by plotting diverting medium tone (a_(Cj)*,b_(Cj)*) (j=1 to 3) (white circles) and diverted medium tone (a_(Sj)*,b_(Sj)*) (j=1 to 3) (black circles) in an a*b* plane. Since thediverting medium and a diverted medium have mutually different tone, thediverting medium tone (a_(Cj)*, b_(Cj)*) and the diverted medium tone(a_(Sj)*, b_(Sj)*) do not completely coincide with each other. In StepS21, the diverting medium tone (a_(C)*, b_(C)*) (white triangle) iscalculated by summing up the diverting medium tone (a_(Cj) b_(Cj)*) (j=1to 3) while the diverting medium tone (a_(Cj)*, b_(Cj)*) (j=1 to 3) isregarded as a position vector from the origin a % b=0 as in Equation(34).

$\begin{matrix}{{\left( {a_{C}^{*},b_{C}^{*}} \right) = \left( {{\sum\limits_{j = 1}^{3}a_{Cj}^{*}},{\sum\limits_{j = 1}^{3}b_{Cj}^{*}}} \right)}{\left( {a_{S}^{*},b_{S}^{*}} \right) = \left( {{\sum\limits_{j = 1}^{3}a_{Sj}^{*}},{\sum\limits_{j = 1}^{3}b_{Sj}^{*}}} \right)}} & (34)\end{matrix}$

Moreover, difference tone (a_(D*), b_(D*)) is calculated by subtractingthe diverted medium tone (a_(S)*, b_(S)*) (black triangle) from thediverting medium tone (a_(C)*, b_(C)*) (white triangle) as in Equation(35).

(a _(D) *,b _(D)*)=(a _(C) *−a _(S) *,b _(C) *−b _(c)*)  (35)

If the difference tone a_(D)*, b_(D)* can be calculated as describedabove, a color phase direction shown by a vector (−a_(D)*, −b_(D)*) withsigns which are opposite to those of the difference tone (a_(D)*,b_(D)*) as a color phase direction of the gray target tone (a_(gt)*,b_(gt)*) (Step S22). That is, the gray target tone (a_(gt)*, b_(gt)*) isa vector obtained by multiplying the vector (−a_(D)*, −b_(D)*) by apositive coefficient k. The size of the coefficient k is set by theuser, for example. In Step S23, the setting information storage module730 stores the gray target tone (a_(gt)*, b_(gt)*) on the setting tableSTB. Moreover, in Step S24, the setting information storage module 730causes the setting table STB to store a valid flag indicating that theink amount converter 710 is valid. By the above processing, the settingtable STB shown in FIG. 5 stores necessary setting information.Thereafter, the procedure proceeds to processing for creating a base LUTfor the diverting medium with reference to the setting table STB. Here,description will be given of a part which is different from theprocessing for creating the base LUT for the basic medium in turn.

First, in Step S100 in FIG. 6, each of the converters 300, 310, 410, and136 and the like the like is prepared (activated) based on theinformation stored on the setting table STB. In the case of a divertingmedium, each of the converters 300, 310, 410, and 136 and the like forthe diverted medium stored on the setting table STB is prepared(activated). That is, since each of the converters 300, 310, 410, and136 and the like is not prepared for the diverting medium, each of theconverters 300, 310, 410, and 136 and the like for the diverted mediumas a basic medium is diverted. In addition, since a valid flag is added,the ink amount converter 710 is activated, and the conversion of the inkamount I_(j) with the use of the aforementioned conversion relationshipbecomes possible.

In the initial setting processing (Step T107 in FIG. 14) in Step T100 inFIG. 13, the gray target tone (a_(gt)*, b_(gt)*)=k×(−a_(D*), −b_(D*))stored on the setting table STB in Step S23 of FIG. 2 is set. That is,while the gray target is always set on the L* axis when the base LUT forthe basic medium is created, the gray target is shifted in the oppositecolor phase direction of relative tone of the diverting medium when thebase LUT for the diverting medium is created.

FIG. 23 is a diagram showing a gray target when the LUT for thediverting medium is created. As shown in the drawing, lattice points(white circles) corresponding to the gray axis lattice points arerestricted so as to indicate positions which equally divides indosixteen parts a line segment connecting a paper black point and a paperwhite point on the L* axis in the L*a*b* color space and curved in thephase color direction of the gray target tone (a_(gt)*, b_(gt)*). In sodoing, positions of the lattice points corresponding to the gray axislattice points after the smoothing processing become positions deviatedfrom the L* axis. The amount of curve becomes a maximum in theintermediate luminosity region, and a maximum value at L*=50 becomes thegray target tone (a_(gt)*, b_(gt)*) in this embodiment. In addition, asingle or a plurality of control points which can be dragged and droppedby the user may be provided on the gray target, and a coefficient kwhich defines the amount of curve which passes through the dragged anddropped control points may be determined.

Moreover, in the optimization processing in Step T130 in FIG. 13, thestandard duty limit value D_(SIj) (j=1 to 8) of each kind of ink for thediverted medium stored on the setting table STB is multiplied by therevision value RW and converted into a new control value (=temporaryduty limit value D_(PI); j=1 to 8). That is, the standard duty limitvalue D_(SIj) (j=1 to 8) of each kind of ink for the diverted mediumstored on the setting table STB is not used as it is as the duty limitvalue for the optimization processing but is used after the conversioninto the temporary duty limit value D_(PIj). Accordingly, theoptimization of the ink amount I_(j) is executed under a restrictioncondition of the'temporary duty limit value D_(PIj). Therefore, theprocessing in Step T130 executed after the diverting medium isdesignated corresponds to the ink amount determining step in which imagequality by the designated ink amount is evaluated with a predictionresult of the hue value by the color prediction model with which it ispossible to predict the hue value when the designated amount of ink ismade to adhere to the diverted medium and an ink amount below the newlimit value is designated to execute prediction of the hue value by thecolor prediction model when the ink amount which reproduces the huevalue shown by the lattice point is determined in the optimization ofthe ink amount based on the evaluation. In addition, Steps S17 and S18and Step T130 also correspond to the limit value determining step inwhich the second hue value feature is corrected and approximated to thefirst hue feature and a new limit value for the ink amount is determinedbased on the second hue value feature after the approximation.

Here, the revision value RW is a value which is 1.0 or less or more asdescribed above. When the revision value is equal to or less than 1.0,the temporary duty limit value D_(PIj) becomes equal to or less than thestandard duty limit value D_(SIj). Therefore, it is possible to optimizethe ink amount I_(j) within a range of the ink amount I_(j) in whicheach of the converters 300, 310, 410, and 136 and the like for thediverted medium can predict the hue value and the like.

On the other hand, when the revision value RW is greater than 1.0, thetemporary duty limit value D_(PIj) becomes a value which is greater thanthe standard duty limit value D_(SIj). In such a case, there may be inkamounts I_(j) which exceed a range (within the standard duty limit valueD_(SIj)) of the ink amount I_(j) (j=1 to 8), in which it is possible topredict the hue value and the like by the converter, among the inkamounts I_(j) input to the forward model converter 300 and the imagequality evaluation index converter 136 for the diverted medium. If anink amount I_(j) which exceeds the range of the ink amount I_(j) (j=1 to8), in which the converters can predict the hue value and the like, isinput to the forward model converter 300 and the image qualityevaluation index converter 136 for the diverted medium as describedabove, prediction results for the hue values and the like are ruined,and optimization of the ink amount I_(j) cannot substantially beexecuted, in some cases.

According to this embodiment, the ink amount optimization module 134thus reduces the ink amount I_(j) (j=1 to 8) based on the designated inkamount I_(j) to the standard duty limit value D_(SIj) when the inkamount I_(j) (j=1 to 8) based on the designated ink amount I_(j) (j=1 to4) exceeds the standard duty limit value D_(SIj) and executesoptimization processing of the ink amount including prediction and thelike of the hue value by the forward model converter 300 and the imagequality evaluation index converter 136 for the diverted medium based onthe reduced ink amount in the optimization processing in Step T130.

FIG. 24 is a diagram showing an example of a state in which the inkamount is reduced. FIG. 24 shows an example of an ink amount space withtwo axes of two types of primary ink (described as ink 1 and ink 2),where the horizontal axis represents an ink amount of the ink 1, and thevertical direction represents an ink amount of the ink 2. In addition,the inside of a chain line in FIG. 24 represents a region within thestandard duty limit value D_(Sij) (j=5) for the secondary ink amount(I₅, for example) by the ink 1 and the ink 2. When the ink amount of thesecondary color based on the designated ink amount I_(j) exceeds thestandard duty limit value for the secondary color as shown by whitecircles in FIG. 24, the ink amount optimization module 134 reduces theink amount of the secondary color to the ink amount (black circles onthe chain line in FIG. 24) at positions which are in contact with thestandard duty limit value in the ink amount space. By such reduction,the ink amounts of the ink 1 and the ink 2 constituting the secondarycolor are reduced, and at least a situation in which the ink amounts ofthe secondary color exceed the standard limit value for the secondarycolor can be solved. Although the description was given of a certainsecondary color in FIG. 24, all ink amounts I_(j) (j=1 to 8) based onthe designated ink amount I_(j) (j=1 to 4) are compared with thestandard duty limit values D_(SIj), and reduction is performed, ifnecessary, such that all ink amounts I_(j) (j=1 to 8) do not exceedcorresponding reference duty limit values.

When the ink amount is reduced as described above, the reductiondirection of the ink amount is a direction toward the origin (a point atwhich the ink amount is Zero) in the ink amount space (see an arrow inFIG. 24). The same is true when the ink amount I₈ of the tertiary coloris reduced. By performing reduction in such a direction, it is possibleto substantially maintain the tone by the ink amount before and afterthe reduction. In the optimization processing in Step T130, the inkamount optimization module 134 may not always reduce the ink amountI_(j) (j=1 to 8) based on the designated ink amount I_(j) (j=1 to 4) tothe standard duty limit value D_(SIj) but may reduce the ink amount (j=1to 8) based on the designated ink amount I_(j) (j=1 to 4) to an inkamount which is smaller than the standard duty limit value D_(SIj) inaccordance with the difference with the standard duty limit valueD_(SIj), when the ink amount I_(j) (j=1 to 8) based on the designatedink amount I_(j) (j=1 to 4) exceeds the standard duty limit valueD_(SIj).

As an example of this case, a case is assumed in which both the inkamount I_(5a) of the secondary color based on a certain designated inkamount I_(j) and the ink amount I_(5b) of the secondary color based onanother designated ink mount exceed the standard duty limit valueD_(SI5), as shown in FIG. 24. Since the distance from the ink amountI_(5a) to the standard duty limit value D_(SI5) is equal to or longerthan a predetermined distance, the ink amount I_(5a) is reduced to(sticks to) the standard duty limit value D_(SI5) as described above. Onthe other hand, the ink amount which departs from the standard dutylimit value D_(SI5) by a distance which is less than the predetermineddistance is reduced to an ink amount which is smaller than the standardduty limit value D_(SI5) (a black circle further inside than the chainline in FIG. 24). In such a case, the ink amount is converted (reduced)to an ink amount at a position further from the standard duty limitvalue D_(SI5) (closer to the origin zero) when the distance to thestandard duty limit value D_(SI5) is shorter. With such a configuration,it is possible to prevent lack or failure of the gradation feature inthe base LUT generated after the ink amount optimization processing.

Furthermore, in the creation of the base LUT in Step S400 in FIG. 6, theink amount I_(j) (j=1 to 4) corresponding to each lattice point finallyobtained by the smoothing and optimization processing is not registeredas it is as the output value of the base LUTs 510 and 520 but convertedbased on the conversion relationship set in the ink amount converter 710for each type of primary color and then registered as the output valueof the base LUTs 510 and 520 after the conversion. Each of theconverters 300, 310, 410, and 136 and the like for the diverted mediumis for outputting a prediction result corresponding to a hue valuefeature of each ink on the diverted medium. For example, it is assumedthat an ink amount I_(4m) of the K ink shown in FIG. 20A is determinedas an optimal ink amount I_(4m) and optimized for a certain latticepoint, for example. At this time, it is possible to understand that theink amount I_(4m) is optimal and the color formation by the ink amount,namely the luminosity L*=50 which is reproduced by the amount I_(4m) ofK ink is optimal, for the lattice point.

Although the amount of K ink which can reproduce optimal luminosity L*on the diverted medium is I_(4m), the amount of K ink which canreproduce the same optimal luminosity L* on the diverting medium is notI_(4m). That is, not the amount L_(4m) of K ink which can reproduceoptimal luminosity L* on the diverted medium but the amount of K inkwhich can reproduce the same optimal luminosity L* on the divertingmedium is a truly optimal ink amount for the diverting medium. Theamount of K ink which can reproduce the same optimal luminosity L* onthe diverting medium can be obtained by converting the amount I_(4m) ofK ink which can reproduce the optimal luminosity L* on the diverted,medium based on the conversion relationship. Accordingly, it is possibleto obtain the base LUTs 510 and 520 in which the optimal ink amountI_(j) is defined for the diverting medium by registering the optimal inkamount I_(j) obtained by converting the ink amount I_(j) of each latticepoint which is finally obtained by the smoothing and the optimizationprocessing, as the output value of the base LUTs 510 and 520. That is,Step S400 corresponds to a profile creating step in which the ink amountdetermined by the optimization is converted by the conversionrelationship based on the first hue value feature and the second huevalue feature and a profile for the second printing medium for which theconverted ink amount has been defined is created.

By displaying the weight designation UI image shown in FIG. 3, theweight w_(L*), w_(a*) . . . of the object function E for optimizing theink amount I_(j) is set to the default weight w_(L*), w_(a*) . . . whichis suitable for the group of the diverting medium as long as the userdoes not change the setting. Therefore, it is possible to create thebase LUTs 510 and 520 which place values on the image quality suitablefor the group of the diverting medium. By displaying the weightdesignation UI image after the medium designation, it is possible to setthe weight w_(L*), w_(a*) . . . in accordance with the properties anduse purpose of the medium.

Incidentally, since the diverting medium and the diverted medium have adifferent tone, a deviation occurs in the prediction result by theforward model converter 300 (spectral printing model converter 310). Itis a matter of course that a deviation also occurs in the predictionresult of the hue values around the L* axis in accordance with the toneof the diverting medium and the diverted medium. On the other hand,since the gray target tone (a_(gt)*, b_(gt)*) is intentionally deviatedin an opposite color phase direction to the difference tone (a_(D)*,b_(D)*) between the diverting medium and the diverted medium in thisembodiment, it is possible to allow true hue values (not the hue valuespredicted by the forward model converter 300 but the hue valuesreproduced when the amounts I_(j) of ink corresponding to the latticepoints are made to adhere to the diverting medium) of the lattice pointscorresponding to the gray axis lattice points restricted to the graytarget to be positioned on the L* axis. According to such a base LUT, itis possible to perform interpolating computation with the use of the inkamount I_(j) which can truly reproduce achromatic color (gray).Therefore, according to the color correction LUTs 610 and 620 createdwith the use of interpolating computation based on the base LUTs 510 and520, it is possible to achieve a printing result which is particularlyexcellent in color reproducibility of an achromatic color (gray) and agradation feature. By causing the ROM 51 of the printer 20 to store thecorrection LUTs 610 and 620, color conversion for the diverting mediumbecome possible, and it is possible to execute printing on the divertingmedium.

As described above, according to the embodiment, the hue value feature(luminosity feature) on the diverting medium with respect to the inkamount up to the duty limit value for the diverting medium is correctedand approximated to the hue value feature (luminosity feature) on thediverted medium with respect to the ink amount up to the duty limitvalue for the diverted medium, and a new limit value (temporary dutylimit value) of the ink amount is determined based on the value RWindicated by the maximum ink amount in the luminosity feature after thecorrection. Then, when optimization of the ink amount to be adhered ontothe diverted medium is executed with the use of the prediction result ofthe hue value by the forward model converter 300 and the like preparedcorresponding to the diverted medium, the ink amount is optimized withinthe temporary duty limit value (optimal ink amount is determined).Therefore, the base LUT for the diverting medium generated by convertingthe thus determined ink amount based on the conversion relationshipdefines an optimal ink amount for reproducing the same hue value as thehue value reproduced with the optimal ink amount in the diverted medium(with high evaluation by the object function E), and each hue valuereproduced by the ink amount is less one-sided in the color space (forexample, there is no inconvenience in that only the ink amounts whichreproduce relatively dark colors on the diverting medium are defined bythe base LUT). In so doing, it is possible to appropriately executecolor management and further profile creation with the use of thecreated base LUT for the diverting medium.

According to the embodiment, it is possible to obtain the second huevalue feature (luminosity feature) with a high degree of approximationwith respect to the first hue value feature (luminosity feature) withina specific luminosity range in which gradation feature is particularlyvalued. Therefore, it is possible to obtain the base LUT for thediverting medium, in which optimal ink amount for reproducing on thediverting medium the same luminosity change as the satisfactoryluminosity change reproduced with the optimal ink amount (with highevaluation by the object function E) on the diverted medium when thebase LUT for the diverting medium is created as described above, bydetermining the temporary duty limit value based on the second hue valuefeature after the approximation and optimizing the ink amount within theduty limit value.

Furthermore, according to the embodiment, if the designated ink amountexceeds the temporary duty limit value when the optimization of the inkamount to be made to adhere to the diverted medium is executed with theuse of the hue value prediction result and the like by the forward modelconverter 300 and the like prepared corresponding to the divertedmedium, the designated ink amount is reduced to the standard duty limitvalue for the diverted medium, and hue value prediction and the like isperformed on the ink amount after the reduction to search for an optimalink amount. That is, since ink amount search within an ink amount range,in which the forward model converter 300 and the image qualityevaluation index converter 136 can perform hue value prediction andimage quality evaluation, and with the use of the entire ink amountrange is performed, appropriate evaluation of the ink amount isperformed without deteriorating the color prediction result and theimage quality evaluation, and optimal ink amount is determined. Thisresults in creation of an optimal base LUT for the diverting medium.

E. MODIFIED EXAMPLES

The invention is not limited to the above examples and embodiments andcan be performed in various modes within the scope of the gist, and thefollowing modifications can also be made, for example. The aboveembodiments and the modified examples can appropriately be combined.

E-1. Modified Example 1

Here, when a difference between the maximum value of the ink amount inthe first hue value feature (standard duty limit value D_(SIj)) and themaximum value of the ink amount in the second hue value feature (dutylimit value D_(Ij)) is equal to or greater than a predetermined level,there is a case in which the feature difference between the first huevalue feature and the second hue value feature is excessively emphasizedor otherwise becomes excessively small (Step S16 in FIG. 2). If thesecond hue value feature is corrected and approximated to the first huevalue feature in such a state, excessive correction is performed, orotherwise correction is almost not performed at all. Therefore, there isa concern in that it is not possible to achieve a goal of determining anappropriate temporary duty limit value (revision value RW for creatingthe temporary duty limit value) by combining (approximating) theluminosity feature of the diverting medium with the luminosity featureof the diverted medium. Thus, the processing in Step S16 may not beperformed (Step S16 may be executed as in the above embodiment when thedifference between the maximum value of the ink amount in the first huevalue feature (standard duty limit value D_(SIj)) and the maximum valueof the ink amount in the second hue value feature (duty limit valueD_(Ij)) is smaller than the predetermined level).

When Step S16 is not executed, the LUT creation condition setting module700 corrects and approximates the unnormalized second hue value featureto the unnormalized first hue value feature in Step S17. That is,approximate curves as candidates of the second hue value feature afterthe correction are generated by displacing the position of the maximumvalue (duty limit value D_(I4)) of the ink amount in the second huevalue feature along the horizontal axis and displacing the positions ofthe other reference points in the second hue value feature along thehorizontal axis with the displacement of the maximum value position inthe state shown in FIGS. 20A and 21A. A degree of approximation to theunnormalized first hue value feature is evaluated for such approximatecurves, and an approximate curve with the highest degree ofapproximation is fixed as the second hue value feature after thecorrection.

FIG. 25 shows an example of a processing state in Step S17 of themodified example. In FIG. 25, the second hue value feature (luminosityfeature), the first hue value feature (luminosity feature) and thesecond hue value feature after the correction (luminosity feature) areshown as examples by a chain line, a solid line, and a two-dotted chainline, respectively. In Step S18, the LUT creation condition settingmodule 700 sets the maximum value D_(max)′ (see FIG. 25) itself of theink amount in the fixed hue value feature after the correction as thetemporary duty limit value D_(PIj) (j=4) for the ink (K ink) to whichthe thus approximated second hue value feature corresponds. In addition,the temporary duty limit v values D_(PIj) (j=1 to 3, 5 to 8) for otherkinds of ink are calculated by multiplying the standard duty limitvalues D_(SIj) (j=1 to 3, 5 to 8) for the other kinds of ink by a ratio(D_(PI4)/D_(SI4)) between the duty limit value D_(PIj) (j=4) and thestandard duty limit value D_(SIj) (j=4). That is, according to thismodified example, the revision value RW becomes D_(PI4)/D_(SI4) (here,D_(PI4)=D_(max)′). The temporary duty limit value D_(PIj) (j=1 to 8)obtained for each of the revision values RW or the corrected ink amountsI_(j) (j=1 to 8) is stored on the setting table STB. In the optimizationprocessing in Step T130 in FIG. 13, optimization of the ink amount I_(j)is executed under restriction of the temporary duty limit value D_(PIj)(j=1 to 8).

E-2. Modified Example 2

In the above description, the ink amount I_(j) (j=1 to 4) determined bythe optimization of the ink amount on the assumption of the feature ofthe diverted medium is converted based on the conversion relationshipfor compensating for the feature difference between the first hue valuefeature and the second hue value feature and then registered as anoutput value of the base LUTs 510 and 520 when the base LUTs 510 and 520for the diverting medium is created. However, a value converted bymultiplying the ink amount I_(j) (j=1 to 4) determined by theoptimization as described above by the ratio D_(Ij)/D_(PIj); j=1 to 4)between the duty limit value for the diverting medium and the temporaryduty limit value may be registered as an output value of the base LUTs510 and 520. In so doing, it is possible to convert the ink amountoptimized under the temporary duty limit value into the ink amountwithin a range available for the ink amount on the diverting medium.However, since the ink amount is substantially determined by theoptimization up to the standard duty limit value when the temporary dutylimit value>standard duty limit value for the diverted medium issatisfied, a value converted by multiplying the ink amount I_(j)determined as described above by the ratio (D_(Ij)/D_(SIj); j=1 to 4)between the duty limit value for the diverting medium and the standardduty limit value may be registered as an output value of the base LUTs510 and 520.

E-3. Modified Example 3

FIG. 26 is a diagram showing a medium feature designation UI image. Thedrawing shows hue value features (C*, L*) of the diverted medium and thediverting medium. In general, when ink of about the duty limit valueD_(Ij) is made to adhere to each medium, there is no variation in colorformation if more ink is made to adhere. Therefore, an ink amount I_(j)at which absolute values of inclination of the C* value and the L* valuebecome equal to a predetermined reference value (≈0) may be set as theduty limit value D_(Ij). In the example in FIG. 26, a marker (whitetriangle) is displayed at the ink amount I_(j) at which the absolutevalue of the inclination becomes equal to the reference value in thegraph of the hue value feature. In so doing, the user can recognize towhich ink amount the duty limit value D_(Ij) is set. In the example inFIG. 26, it is possible for the user to directly designate the dutylimit value D_(Ij) by selection of a radio button. In so doing, it ispossible to handle a case in which a marker position is obviouslydifferent from the ink amount I_(j) of the color patch in which the userobserves the ink bleeding.

E-4. Modified Example 4

Although the CIE-Lab color system is used as a device-independent colorsystem in the above embodiment, it is possible to use another arbitrarydevice-independent color system such as a CIE-XYZ color system, aCIE-L*u*v* color system, or the like. However, it is preferable to use adevice-independent color system such as a CIE-Lab color system, aCIE-L*u*v* color system, or the like, which is a uniform color system,from a viewpoint of realizing smooth color reproduction.

E-5. Modified Example 5

Although the processing with the use of the dynamic model is employed asthe smoothing, another kind of smoothing may also be employed. Forexample, it is possible to employ smoothing in which intervals betweenadjacent hue values are measured and individual intervals are adjustedso as to be close to the average value thereof, for example.

E-6. Modified Example 6

The “ink” in this specification is not limited to liquid ink used in anink jet printer, an offset printing, or the like and is used with a widemeaning including a toner used in a laser printer. As another termincluding such a wide meaning of “ink”, it is possible to use the term“color material”, “coloring material”, or “coloring agent”.

E-7. Modified Example 7

In the above embodiment, the description was given of a method and anapparatus for creating a color conversion profile as a look-up table,but the embodiment of the invention can also be applied to a printingapparatus manufacturing system provided with an installing unit whichinstalls the thus obtained color conversion profile on a printingapparatus. The color conversion profile creating apparatus for creatingthe color conversion profile may be included in the printing apparatusmanufacturing system or may be included in another system or apparatus.In addition, the installing unit of the manufacturing system can berealized as an installer (install program) of a printer driver, forexample.

The entire disclosure of Japanese Patent Application No. 2011-048169,filed Mar. 4, 2011 is expressly incorporated by reference herein.

1. A profile creation method according to which a profile of defining anink amount is created by determining an ink amount for reproducing a huevalue indicated by a lattice point in a device-independent color system,the method comprising: firstly obtaining a first hue value featurerepresenting a variation in a hue value on a first print mediumcorresponding to a variation in an ink amount up to a limit value of anink amount which can adhere to the first print medium; secondlyobtaining a second hue value feature representing a variation in a huevalue in a second print medium, which is different from the first printmedium, corresponding to a variation in an ink amount up to a limitvalue of an ink amount which can adhere to the second print medium;determining a new limit value of the ink amount based on the second huevalue feature after approximation by correcting and approximating thesecond hue value feature to the first hue value feature; determining anink amount which is equal to or less than the newly determined limitvalue to execute optimization when the ink amount for reproducing thehue value indicated by the lattice point is determined by the ink amountoptimization with the use of an object function for evaluating imagequality when a designated amount of ink is made to adhere to the firstprint medium; and creating a profile for the second print medium, forwhich the converted ink amount has been defined, by converting the inkamount determined by the optimization with a conversion relationshipbased on the first hue value feature and the second hue value feature.2. The profile creation method according to claim 1, wherein indetermining the limit value, the new limit value is determined based ona maximum value of the ink amount in the second hue value feature afterthe approximation.
 3. The profile creation method according to claim 1,wherein in determining the limit value, curves are generated based oneach reference point after displacement, by displacing a plurality ofreference points in the second hue value feature in an ink amountdirection, degrees of approximation between the generated curves and thefirst color hue value feature are evaluated, and a curve with thehighest degree of approximation is regarded as the second hue valuefeature after the approximation.
 4. The profile creation methodaccording to claim 3, wherein in determining the limit value, moreweight at the time of evaluation is given to the reference pointsbelonging to a specific hue value range than to the other referencepoints from among a plurality of reference points on the curve and adegree of approximation between the curve and the first hue valuefeature is evaluated.
 5. The profile creation method according to claim4, wherein when the first hue value feature and the second hue valuefeature show luminosity variations corresponding to variations in inkamounts, the weight is given at least to reference points belonging to aspecific intermediate luminosity region from among the plurality ofreference points on the curve in the determining of the limit value. 6.The profile creation method according to claim 1, wherein in determiningthe ink amount, a lattice point to be restricted to an achromatic coloris restricted to a hue value deviated from the achromatic color in acolor phase direction based on a tone difference between the first printmedium and the second print medium.
 7. A recording medium, having aprofile creation program which causes a computer to execute a functionof creating a profile which defines an ink amount by determining an inkamount for reproducing a hue value indicated by a lattice point in adevice-independent color system, comprising: a first obtaining functionof obtaining a first hue value feature representing a variation in a huevalue on a first print medium corresponding to a variation in an inkamount up to a limit value of an ink amount which can adhere to thefirst print medium; a second obtaining function of obtaining a secondhue value feature representing a variation in a hue value in a secondprint medium, which is different from the first print medium,corresponding to a variation in an ink amount up to a limit value of anink amount which can adhere to the second print medium; a limit valuedetermining function of determining a new limit value of the ink amountbased on the second hue value feature after approximation by correctingand approximating the second hue value feature to the first hue valuefeature; an ink amount determining function of designating an ink amountwhich is equal to or less than the newly determined limit value toexecute the optimization when the ink amount for reproducing the huevalue indicated by the lattice point is determined by the ink amountoptimization with the use of an object function for evaluating imagequality when a designated amount of ink is made to adhere to the firstprint medium; and a profile creating function of creating a profile forthe second print medium, for which the converted ink amount has beendefined, by converting the ink amount determined by the optimizationwith a conversion relationship based on the first hue value feature andthe second hue value feature.
 8. A printing apparatus which causes anamount of ink, which has been obtained by performing color conversionwith reference to a profile, to adhere to a print medium, wherein theprofile is a profile which is created by determining an ink amount forreproducing a hue value indicated by a lattice point in adevice-independent color system to define an ink amount, which is aprofile for a second print medium created by obtaining a first hue valuefeature representing a variation in a hue value on a first print mediumcorresponding to a variation in an ink amount up to a limit value of anink amount which can adhere to the first print medium, obtaining asecond hue value feature representing a variation in a hue value in asecond print medium, which is different from the first print medium,corresponding to a variation in an ink amount up to a limit value of anink amount which can adhere to the second print medium, determining anew limit value of the ink amount based on the second hue value featureafter approximation by correcting and approximating the second hue valuefeature to the first hue value feature, determining an ink amount whichis equal to or less than the newly determined limit value to execute theoptimization when the ink amount for reproducing the hue value indicatedby the lattice point is determined by the ink amount optimization withthe use of an object function for evaluating image quality when adesignated amount of ink is made to adhere to the first print medium,and creating a profile for the second print medium, for which theconverted ink amount has been defined, by converting the ink amountdetermined by the optimization with a conversion relationship based onthe first hue value feature and the second hue value feature.